Research Papers & BOOKS (by Salah-Eddine KABBAJ) _____________________________
[1] La formule de la dimension pour les S-domaines forts
universels.
Bollettino dell'Unione Matematica Italiana Algebra e Geometria, VI,
vol V-D (1) (1986) 145-161.
[2] Examples of Jaffard domains (with A. Bouvier).
Journal
of Pure and Applied Algebra 54 (1988) 155-165. [PDF]
[3] On Jaffard domains (with D. F. Anderson, A. Bouvier, D.
Dobbs and M. Fontana).
Expositiones Mathematicae 6 (1988) 145-175. [PDF]
[4] Universally catenarian domains of D+M type (with D.
Anderson, D. Dobbs and S. B. Mulay).
Proceedings of the American Mathematical
Society 104 (2) (1988) 378-384. [PDF]
[5] Sur une conjecture de Malik et Mott.
Pub. Math. Lyon I
series 3/B (1988) 13-19.
[6] Sur l'anneau factoriel non noetherien de Fujita.
Proceedings of Rome Conference (Italy) (1989) 125-130.
[7] On the Krull and valuative dimension of D+ XDS[X]
domains (with M. Fontana).
Journal of Pure and Applied Algebra 63 (1990)
231-245. [PDF]
[8] Une conjecture sur les anneaux de Nagata.
Journal of
Pure and Applied Algebra 64 (1990) 263-268. [PDF]
[9] Direct limits of Jaffard domains and S-domains (with D.
Dobbs and M. Fontana).
Comment. Math. Univ. St. Paul. 39 (2) (1990)
143-155. [PDF]
[10] Sur les S-domaines forts de Kaplansky.
Journal of
Algebra 137 (2) (1991) 400-415. [PDF]
[11] Krull and valuative dimension of the rings of the form
A+XB[X] (with M. Fontana and L. Izelgue).
Lecture Notes in Pure and Applied
Mathematics Dekker 153 (1993) 111-130. [PDF]
[12] Quelques proprietes des chaines d'ideaux dans les
anneaux A+XB[X] (with M. Fontana and L. Izelgue).
Communications in Algebra 22
(1) (1994) 9-27.
[13] Duals of ideals in pullback constructions (with E.
Houston, T. Lucas and A. Mimouni).
Lecture Notes in Pure and Applied Mathematics
Dekker 171 (1995) 263-276. [PDF]
[14] Dimension of the tensor product of two particular
pullbacks (with F. Girolami).
Math. Appl.,
Kluwer Acad. Publ. 343 (1995) 221- 226.
[15] Sur quelques proprietes des sous-anneaux de la forme D
+ I d'un anneau integre (with Fontana and L. Izelgue).
Communications in Algebra
23 (11) (1995) 4189-4210.
[16] Classes of D+M rings defined by homological conditions
(with D. Costa).
Communications in Algebra 24 (3) (1996) 891-906.
[17] Group rings R[G] with 3-generated ideals when R is
artinian (with S. Ameziane and M. Fontana).
Communications in Algebra 24 (4)
(1996) 1253-1280.
[18] Dimension and valuative dimension of the Serre
conjecture ring R
Lecture Notes in Pure
and Applied Mathematics Dekker 185 (1997) 173-180. [PDF]
[19] Dimension of tensor products of AF-rings (with S.
Bouchiba and F. Girolami).
Lecture Notes in Pure and Applied Mathematics Dekker
185 (1997) 141-154. [PDF]
[20] Duals of ideals in polynomial rings (with E. Houston,
T. Lucas and A. Mimouni).
Lecture Notes in Pure and Applied Mathematics Dekker
185 (1997) 349-358. [PDF]
[21] Some factorization properties of A+XB[X] domains (with
V. Barucci and L. Izelgue).
Lecture Notes in Pure and Applied Mathematics Dekker
185 (1997) 69-78. [PDF]
[22] N-coherent rings and modules (with D.Dobbs and
N.Mahdou).
Lecture Notes in Pure and Applied Mathematics Dekker 185
(1997) 269-282. [PDF]
[23] Group rings R[G] with 4-generated ideals when R is an
artinian principal ideal ring (with S. Ameziane).
Lecture Notes in Pure and
Applied Mathematics Dekker 185 (1997) 1-14. [PDF]
[24] On the Krull dimension of domains of integer-valued
polynomials (with M. Fontana, L. Izelgue, and F. Tartarone).
Expostiones
Mathematicae 15 (1997) 433-465. [PDF]
[25] On the prime spectrum of commutative semi-group rings
(with S. Ameziane and D. Dobbs).
Communications in Algebra 26 (8) (1998)
2559-2589. [PDF]
[26] On the spectrum of a group ring (with S. Ameziane, D.
Costa and S. Zarzuela).
Communications in Algebra 27 (1) (1999) 387-403. [PDF]
[27] Group rings R[G] with 4-generated ideals when R is an
artinian ring with the two generator property (with S. Ameziane).
Lecture Notes
in Pure and Applied Mathematics Dekker 205 (1999) 1-23. [PDF]
[28] The dimension of tensor products of commutative
algebras over a zero-dimensional ring (with S. Bouchiba and F. Girolami).
Lecture Notes in Pure and Applied Mathematics Dekker 205 (1999)
145-159. [PDF]
[29] Trace properties and integral domains (with T. Lucas
and A. Mimouni).
Lecture Notes in Pure and Applied Mathematics Dekker 205
(1999) 421-436. [PDF]
[30] On the class group of A+XB[X] domains (with D.F.
Anderson and S. El Baghdadi).
Lecture Notes in Pure and Applied Mathematics Dekker 205 (1999) 73-85.
[PDF]
[31] When is a D + M an (n, d)-ring? (with D. Dobbs, N.
Mahdou, and M. Sobrani).
Lecture Notes in Pure and Applied Mathematics Dekker
205 (1999) 257-270. [PDF]
[32] Polynomial closure in essential domains and pullbacks
(with M. Fontana, L. Izelgue, and F. Tartarone).
Lecture Notes in Pure and
Applied Mathematics Dekker 205 (1999) 307-321. [PDF]
[33] The dimension of tensor products of k-algebras arising
from pullbacks (with S. Bouchiba and F.Girolami).
Journal of Pure and Applied
Algebra 137 (2) (1999) 125-138. [PDF]
[34] When is the dual of an ideal a ring ? (with E.
Houston, T. Lucas, and A. Mimouni).
Journal of Algebra 225 (1) (2000)
429-450. [PDF]
[35] The dilworth number of group rings over an artin local
ring (with S. Ameziane, J. Okon, and P. Vicknair).
Communications in Algebra 28
(10) (2000) 4596-4610. [PDF]
[36] On the class group of a graded domain (with S.
El-Baghdadi and L. Izelgue).
Journal of Pure and Applied Algebra 171 (2-3)
(2002) 171-184. [PDF]
[37] The homogeneous class group of A+XB[X] domains (with
D. Anderson and S. El-baghdadi).
International Journal of Commutative Rings 1
(1) (2002) 11-25.
[38] Tensor products of Cohen-Macaulay rings. Solution to a
problem of Grothendieck (with S. Bouchiba).
Journal of Algebra 252 (2002)
65-73. [PDF]
[39] On the prime ideal structure of tensor products of
algebras (with S. Bouchiba & D. Dobbs).
Journal of Pure and Applied Algebra
176 (2002) 89-112. [PDF]
[40] Trivial extensions of local rings and a conjecture of
Costa (with N. Mahdou).
Lecture Notes in Pure and Applied Mathematics Dekker 231
(2003) 301–311. [PDF]
[41] Trace properties and pullbacks (with T. Lucas & A.
Mimouni).
Communications in Algebra 31 (3) (2003) 1085-1111. [PDF]
[42] Class semigroups of integral domains (with A.
Mimouni).
Journal of Algebra 264 (2003) 620-640. [PDF]
[43] Trivial
extensions defined by coherent-like conditions (with N. Mahdou).
Communications in Algebra 32 (10) (2004) 3937-3953. [PDF]
[44] Essential
domains and two conjectures in dimension theory (with M. Fontana).
Proceedings of the American Mathematical Society 132 (2004)
2529--2535. [PDF]
[45] On the dimension theory of polynomial rings over pullbacks.
In: Multiplicative Ideal Theory in Commutative Algebra, pp. 263–277, Springer, New York, 2006. [PDF]
[46]
$t$-Class semigroups of integral domains (with A. Mimouni).
J. reine angew. Math. 612 (2007) 213-229. [PDF]
[47] Corrigendum to: “Class semigroups of integral domains” (with A. Mimouni).
Journal of Algebra 320 (2008) 1769–1770. [PDF]
[48] Bouvier's conjecture (with S. Bouchiba).
In: Commutative Algebra and its Applications, W. de Gruyter, Berlin, pp. 79–88, 2009. [PDF]
[49] $t$-Class semigroups of Noetherian domains (with A. Mimouni).
In: Commutative Algebra and its Applications, W. de Gruyter, Berlin, pp. 283–290, 2009. [PDF]
[50] Constituent groups of Clifford semigroups arising from t-closure (with A. Mimouni).
Journal of Algebra 321 (2009) 1443–1452. [PDF]
[51] Trivial extensions defined by Prüfer conditions (with C. Bakkari and N. Mahdou).
Journal of Pure and Applied Algebra 214 (2010) 53–60. [PDF]
[52] Class groups and class semigroups of integral domains (with S. Bazzoni).
In: Commutative Algebra. Noetherian and non-Noetherian Perspectives, Springer, New York, pp. 47–76, 2011. [PDF]
[53] Commutative rings in which every finitely generated ideal is quasi-projective (with J. Abuihlail and M. Jarrar).
Journal of Pure and Applied Algebra 215 (2011) 2504–2511. [PDF]
[54] Integral domains with Boolean t-class semigroups (with A. Mimouni).
Arabian Journal of Mathematics (Springer) 1 (1) (2012) 89-95 [PDF]
[55] On the prime ideal structure of symbolic Rees algebra (with S. Bouchiba).
Journal of Commutative Algebra 4 (3) (2012) 327-343 [PDF]
[56] Weak global dimension of Prüfer-like rings (with K. Adarbeh).
In: Commutative Algebra: Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions, pp. 1–23, Springer, New York, 2014. [PDF]
[57] Regularity of tensor products of k-algebras (with S. Bouchiba).
Mathematica Scandinavica 115 (1) (2014) 5-19 [PDF]
[58] Prüfer conditions in an amalgamated duplication of a ring along an ideal (with M. Chhiti, M. Jarrar, and N. Mahdou).
Communications in Algebra 43 (1) (2015) 249-261 [PDF]
[59] Core of ideals in integral domains (with A. Mimouni).
Journal of Algebra 445 (2016) 327-351. [PDF]
[60] Dimension theory of tensor products of AF-rings.
Palestine Journal of Mathematics 5 (Special Issue 1) (2016) 32-48. [PDF]
[61] On t-reductions of ideals in pullbacks (with A. Kadri and A. Mimouni).
New York Journal of Mathematics 22 (2016) 875-889. [PDF]
[62] Zaks' conjecture on rings with semi-regular proper homomorphic images (with K. Adarbeh).
Journal of Algebra 466 (2016) 169-183. [PDF]
[63] Bi-amalgamations subject to the arithmetical property (with N. Mahdou and M. A. S. Moutui).
Journal of Algebra and its Applications, 16 (2017), no. 2, 1750030, 11 pp. [PDF]
[64] Bi-amalgamated algebras along ideals (with K. Louartiti and M. Tamekkante).
Journal of Commutative Algebra 9 (1) (2017) 65-87. [PDF]
[65] Star-reductions of ideals and Prüfer v-multiplication domains (with E. Houston and A. Mimouni).
Journal of Commutative Algebra 9 (4) (2017) 491-505. [PDF]
[66] Matlis' semi-regularity in trivial ring extensions issued from integral domains (with K. Adarbeh).
Colloquium Mathematicum 150 (2) (2017) 229-241. [PDF]
[67] Embedding dimension and codimension of tensor products of algebras over a field (with S. Bouchiba).
In: Rings, Polynomials, and Modules, pp. 53–77, Springer, New York, 2017. [PDF]
[68] t-Reductions and t-integral closure of ideals (with A. Kadri).
Rocky Mountain Journal of Mathematics 47 (6) (2017) 1875-1899. [PDF]
[69] Zero-divisor graphs of amalgamations (with A. Mimouni).
Mathematica Scandinavica 123 (2018) 174--190. [PDF]
[70] t-Reductions and t-integral closure of ideals in Noetherian domains (with A. Kadri and A. Mimouni).
New York Journal of Mathematics 24 (2018) 404-418. [PDF]
[71] Prüfer conditions in the Nagata ring and the Serre's conjecture ring (with M. Jarrar).
Communications in Algebra 46 (5) (2018) 2073-2082. [PDF]
[72] On t-Reduction and t-integral closure of ideals in integral domains.
In: Advances in Commutative Algebra, pp. 135-158, Birkhäuser, Singapore, 2019. [PDF]
[73] Reductions of ideals in pullbacks (with A. Mimouni).
Algebra Colloquium 27 (2020) 523-530. [PDF]
[74] Core of ideals in one-dimensional Noetherian domains (with A. Mimouni).
Journal of Algebra 555 (2020) 346-360. [PDF]
[75] Trivial extensions subject to semi-regularity and semi-coherence (with K. Adarbeh).
Quaestiones Mathematicae 43 (2020) 45-54. [PDF]
[76] Minimal reductions and core of ideals in pullbacks (with A. Mimouni).
Acta Mathematica Hungarica 163 (2021) 512-529. [PDF]
[77] Linkage of ideals in integral domains (with A. Mimouni).
Algebra and Representation Theory 24 (2021) 799-809. [PDF]
[78] Regularity and related properties in tensor products of algebras over a field (with F. Suwayyid)
Springer Proc. Math. Stat. 382 (2021) 171-194.
[79] On the finiteness of Ext-indices of ring extensions (with S. Bouchiba).
Rocky Mountain Journal of Mathematics 52 (2022) 1969-1981.
[80] Reductions and cores of ideals in trivial ring extensions (with A. Mimouni).
Journal of Algebra and its Applications 22 (2023), no. 7, 2350159, 14 pp.
[81] Reductions of ideals in Prüfer rings (with M. Jarrar).
Journal of Commutative Algebra 15 (2023) 45-54.
BOOKS _____________________________
[1] Commutative Ring Theory (with P.-J. Cahen, D. Costa, and M. Fontana)
Lecture Notes in Pure and Applied Mathematics, Vol. 153
Marcel Dekker, New York, 1994.
(280 pages) (ISBN: 0-8247-9170-3)
[2] Commutative Ring Theory II (with P.-J. Cahen, M. Fontana, and E. Houston)
Lecture Notes in Pure and Applied Mathematics, Vol. 185
Marcel Dekker, New York, 1997.
(488 pages) (ISBN: 0-8247-9815-5)
[3] Advances in Commutative Ring Theory (with D. Dobbs & M. Fontana)
Lecture Notes in Pure and Applied Mathematics, Vol. 205
Marcel Dekker, New York, 1999.
(576 pages) (ISBN: 0-8247-7147-8)
[4] Commutative Ring Theory and Applications (with M. Fontana and S. Wiegand)
Lecture Notes in Pure and Applied Mathematics, Vol. 231
Marcel Dekker, New York, 2003.
(494 pages) (ISBN: 0-8247-0855-5)
[5] Commutative Algebra and its Applications (with M. Fontana, B. Olberding, and I. Swanson)
de Gruyter Proceedings in Mathematics
Walter de Gruyter, Berlin, New York, 2009.
(386 pages) (ISBN: 978-3-11-020746-0)
[6] Commutative Algebra. Noetherian and Non-Noetherian Perspectives (with M. Fontana, B. Olberding, and I. Swanson)
Springer, New York, Dordrecht, Heidelberg, London, 2011.
(492 pages) (ISBN: 978-1-4419-6989-7)