Maher Zayed - Academia.edu (original) (raw)

Papers by Maher Zayed

Logic Journal of IGPL, 2012

In this article, the notion of purely large structure is introduced. It is shown, with the aid of... more In this article, the notion of purely large structure is introduced. It is shown, with the aid of a Theorem of Rothmaler, that any finitely accessible class possesses purely large structures. This applies to the class Mod(R) of all left modules over a given ring R. The theory T ∗ of purely large modules is always complete. It is shown that T ∗ is model-complete if and only if R is regular. For any algebra of finite representation type R, over an infinite field, T ∗ is axiomatizable by one sentence over Th(Mod(R)). A characterization of pure semisimple rings, in terms of purely large modules, is obtained.

Communications in Algebra, Aug 23, 2007

Http Www Theses Fr, 1988

Il s'agit d'une etude concernant la theorie des representations d'algebres de dimensi... more Il s'agit d'une etude concernant la theorie des representations d'algebres de dimension finie. Les techniques utilisees sont les ultraproduits de structures algebriques. Nous demontrons (a l'aide d'un theoreme de nazarova-roiter) que la classe des algebres de representation finie sur des corps algebriquement clos coincide avec la classe des algebres closes. En utilisant les ultrafiltres alpha **(+)- bons, alpha >ou= x::(0), une caracterisation des algebres artiniennes de representation finie est etablie. Ce resultat permet d'obtenir un theoreme relatif a la deuxieme conjecture de brauer-thrall. Nous demontrons que les algebres semi-serielles de longueur d, d appartient a in, forment une classe fini-axiomatisable. En introduisant les modules s-pur-projectifs, nous caracterisons les systemes finis de modules indecomposables de type fini sur des algebres connexes infinies. Les ultraproduits sont utilises pour construire une infinite de modules n'ayant aucun facteur direct de type fini. Ainsi, diverses caracterisations des algebres de representation finie sont donnees. Enfin, en utilisant les suites de auslander-reiten, nous etudions les modules indecomposables sur des anneaux purs semi-simples a droite

In the present paper, a semimodule M over a semiring R is called absolutely pure if it is pure in... more In the present paper, a semimodule M over a semiring R is called absolutely pure if it is pure in every semimodule containing it as a subsemimodule. Some well-known properties of absolutely pure modules are extended to semimodules. We introduce and study two particular subclasses of absolutely pure semimodules, namely strongly absolutely pure (SAP) and …nitely injective (f-injective) semimodules. When the semiring R is additively idempotent ,the SAP R semimodules are exactly the f-injective semimodules.A characterization of Fieldhouse regular semimodules is obtained.

Lecture Notes in Mathematics, 1982

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1993

SynopsisIt is shown that for each v ∊ {0, 1, 2}, the class of v-primitive near-rings is not axiom... more SynopsisIt is shown that for each v ∊ {0, 1, 2}, the class of v-primitive near-rings is not axiomatisable.

Monatshefte f�r Mathematik, 1988

The aim of this paper is to prove the following result. If A is a fight pure semisimple ring, the... more The aim of this paper is to prove the following result. If A is a fight pure semisimple ring, then it satisfies one of the two following statements: (a) For any positive integer n, there are at most finitely many indecomposable right modules of length n; or (b) There is an infinite number of integers d such that, for each d, A has infinitely many indecomposable right modules of length d. The result is derived with the aid of ultraproduct-technique.

Monatshefte f�r Mathematik, 1990

The aim of this note is to prove that an artin algebra (resp. a finite dimensional algebra over a... more The aim of this note is to prove that an artin algebra (resp. a finite dimensional algebra over an algebraically closed field) all of whose algebraically compact (resp. E-algebraically compact) indecomposable modules are finitely generated must be of finite-representation type. The result is derived with the aid of a theorem of Ziegler.

Logic Journal of IGPL, 2007

ABSTRACT In this note, we prove that the theory T of cancellative semimodules over a semiring R h... more ABSTRACT In this note, we prove that the theory T of cancellative semimodules over a semiring R has the amalgamation property. If R is an entire cancellative zerosumfree semiring, then T has no model-companion. In particular, the theory of commutative additively cancellative monoids forms an example of a non-companionable theory.

Journal of Pure and Applied Algebra, 1994

Zayed, M., Tensor functors and finite representation type, Journal of Pure and Applied Algebra 93... more Zayed, M., Tensor functors and finite representation type, Journal of Pure and Applied Algebra 93 (1994) 227-229. Let A be a finite-dimensonal algebra over an infinite field K and Mod(A) be the category of all (left) A modules.

Journal of Algebra and Its Applications, 2002

In the present paper, modules which are subisomorphic (in the sense of Goldie) to their pure-inje... more In the present paper, modules which are subisomorphic (in the sense of Goldie) to their pure-injective envelopes are studied. These modules will be called almost pure-injective modules. It is shown that every module is isomorphic to a direct summand of an almost pure-injective module. We prove that these modules are ker-injective (in the sense of Birkenmeier) over pure-embeddings. For a coherent ring R, the class of almost pure-injective modules coincides with the class of ker-injective modules if and only if R is regular. Generally, the class of almost pure-injective modules is neither closed under direct sums nor under elementary equivalence. On the other hand, it is closed under direct products and if the ring has pure global dimension less than or equal to one, it is closed under reduced products. Finally, pure-semisimple rings are characterized, in terms of almost pure-injective modules.

Glasgow Mathematical Journal, 1994

In the present note, Σr denotes the class of all right pure semisimple rings (= right pure global... more In the present note, Σr denotes the class of all right pure semisimple rings (= right pure global dimension zero). It is known that if R ∈ Σr, then R is right artinian and every indecomposable right R-module is finitely generated. The class Σr is not closed under ultraproducts [4]. While Σr is closed under elementary descent (i.e. if S ∈ Σr and R is an elementary subring of S then R ∈ σr) [4], it is an open question whether right pure-semisimplicity is preserved under the passage to ultrapowers [4, Prob. 11.16]. In this note, this question is answered in the affirmative.

Communications in Algebra, 1997

Communications in Algebra, 1988

Archiv der Mathematik, 2001

Abstract.Let R be a right near-ring with identity and Mn(R) be the near-ring of n×n matrices over... more Abstract.Let R be a right near-ring with identity and Mn(R) be the near-ring of n×n matrices over R in the sense of Meldrum and Van der Walt. In this paper, Mn(R) is said to be sigma\sigmasigma-generated if every n×n matrix A over R can be expressed as a sum of elements of Xn(R), where Xn(R)=fijr,∣,1leqqi,jleqqn,rinRX_n(R)=\{f_{ij}^r\,|\,1\leqq i, j\leqq n, r\in R\}Xn(R)=fijr,∣,1leqqi,jleqqn,rinR, is the generating set of Mn(R). We say that R is sigma\sigmasigma-generated if Mn(R) is sigma\sigmasigma-generated for every natural number n. The class of sigma\sigmasigma-generated near-rings contains distributively generated and abstract affine near-rings. It is shown that this class admits homomorphic images. For abelian near-rings R, we prove that the zerosymmetric part of R is a ring, so the class of zerosymmetric abelian sigma\sigmasigma-generated near-rings coincides with the class of rings. Further, for every n, there is a bijection between the two-sided subgroups of R and those of Mn(R).

Archiv der Mathematik, 1988

Archiv der Mathematik, 2002

Let R be a ring. A right R-module M is called f-projective if Ext 1 (M, N) = 0 for any f-injectiv... more Let R be a ring. A right R-module M is called f-projective if Ext 1 (M, N) = 0 for any f-injective right R-module N. We prove that (F-proj, F-inj) is a complete cotorsion theory, where F-proj (F-inj) denotes the class of all f-projective (f-injective) right R-modules. Semihereditary rings, von Neumann regular rings and coherent rings are characterized in terms of f-projective modules and f-injective modules.

Communications in Algebra, 2003