**
Research Papers
& B****OOKS
(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+ XD_{S}[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.**

**[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.

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

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

**
[66]**
Star-reductions of ideals and Prüfer v-multiplication domains (with E. Houston and
A. Mimouni).

**Journal of Commutative Algebra** to
appear. [**PDF**]

**
[67]**
Matlis' semi-regularity in trivial ring extensions issued from integral domains (with K.
Adarbeh).

**Colloquium Mathematicum**, to
appear.
[**PDF**]

**
[68]**
Embedding dimension and codimension of tensor products of algebras over a field (with
S. Bouchiba).

**Rings, Polynomials, and Modules**,
Springer, New York, pp. 1–25, to
appear. [**PDF**]

**
[69]**
Zero-divisor graphs of amalgamations (with
A. Mimouni).

**Mathematica Scandinavica**, to
appear. [**PDF**]

**
[70]**
Prüfer conditions in the Nagata ring and the Serre's conjecture ring (with
M. Jarrar).

**Communications in Algebra**, 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)