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 (with P.-J. Cahen and Z. Elkhayyari).
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.

Multiplicative Ideal Theory in Commutative Algebra, Springer, pp. 263–277, 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).

Commutative Algebra and its Applications, W. de Gruyter, Berlin, pp. 79–88, 2009. [PDF]

 

[49] $t$-Class semigroups of Noetherian domains (with A. Mimouni).

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).

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).

Commutative Algebra: Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions, Springer, New York, pp. 1–23, 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] Star-reductions of ideals and Prüfer v-multiplication domains (with E. Houston and A. Mimouni).

Journal of Commutative Algebra, to appear. [PDF]

 

[64] Bi-amalgamated algebras along ideals (with K. Louartiti and M. Tamekkante).

Journal of Commutative Algebra, to appear. [PDF]

 

[65] Bi-amalgamations subject to the arithmetical property (with N. Mahdou and M. A. S. Moutui). 

Journal of Algebra and its Applications, to appear.  [PDF]

 

 [66] t-Reductions and t-integral closure of ideals (with A. Kadri)

Rocky Mountain Journal of Mathematics, to appear. [PDF]

 

 

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)