Leila Shahbaz

Leila Shahbaz
University of Maragheh · Department of Mathematics

Associate Professor
Head of Department of Mathematics

About

28
Publications
2,109
Reads
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70
Citations
Citations since 2016
9 Research Items
22 Citations
20162017201820192020202120220123456
20162017201820192020202120220123456
20162017201820192020202120220123456
20162017201820192020202120220123456
Additional affiliations
September 2008 - November 2015
University of Maragheh
Position
  • Professor (Associate)
October 2004 - September 2008
Shahid Beheshti University
Position
  • PhD Student

Publications

Publications (28)
Article
Full-text available
In this paper, first the congruences in the category PosAct-S of all poset acts over a pomonoid S; an S-act in the category Pos of all posets, with action preserving monotone maps between them, are introduced. Then, we study the existence of the free and cofree objects in the category PosAct-S. More precisely, we consider all forgetful functors bet...
Article
Injectivity is one of the useful notions in algebra, as well as in many other branches of mathematics, and the study of injectivity with respect to different classes of monomorphisms is crucial in many categories. Also, essentiality is an important notion closely related to injectivity. Down closed monomorphisms and injectivity with respect to thes...
Article
Full-text available
In this paper, we study the categorical and algebraic properties, such as limits and colimits of the category Pos-S with respect to order dense embeddings. Injectivity with respect to this class of monomorphisms has been studied by the author and used to obtain information about injectivity relative to order embeddings. Then, we study three differe...
Poster
Full-text available
In this paper, we define the category PosAct-S of all poset acts; an S-act in the category Pos, with action preserving monotone maps between them. Also, we study the existence of the free and cofree objects in the categories PosAct-S. More precisely, we consider all forgetful functors between these categories and the categories ActS of S-acts, Pos...
Conference Paper
Full-text available
The condition that weak injectivity is equivalent to injectivity is known as the Baer Criterion for injectivity. However, although this condition is true for injectivity of R-modules for every ring R with unit, it is not true for injectivity of S-acts, for an arbitrary monoid S. For example consider (N, max) (see Kilp et al., 2000). Seeking a chara...
Conference Paper
Full-text available
We take ActS to b e the category of right acts over a semigroup S, C to b e an arbitrary closure operator in the category ActS , and M d to b e the class of C-dense monomorphisms resulting from a closure operator C and study injectivity and essen-tialness with respect to the class M d of C-dense monomorphisms. The class of sequentially dense monomo...
Preprint
Injectivity is one of the most central notions in algebra, as well as in many other branches of mathematics and the study of injectivity with respect to different classes of monomorphisms is crucial in almost all categories. Also, essentiality is an important notion closely related to injectivity. In fact, injectivity is characterized and injective...
Article
Full-text available
In this paper, purity of S-posets over a pomonoid S is investigated. We first study some basic properties of absolutely po-pure S-posets. Among other results, it is proved that every regular injective S-poset is absolutely po-pure, and every absolutely po-pure inequationally compact S-poset is regular injective. Then, using the notion of semi-finit...
Article
Full-text available
In this paper, the notion of injectivity with respect to order dense embeddings in the category of S-posets, posets with a monotone action of a pomonoid S on them, is studied. We give a criterion, like the Baer condition for injectivity of modules, or Skornjakov criterion for injectivity of S-sets, for the order dense injectivity. Also, we consider...
Article
Full-text available
No need to say that the study of injectivity with respect to different classes of monomorphisms is crucial in any category. In this paper, the notion of injectivity with respect to down closed embeddings in the category of S-posets, posets with a monotone action of a pomonoid S on them, is studied. We give a criterion, like the Baer condition for i...
Article
Full-text available
Injectivity is one of the central notions in many branches of mathematics. Different kinds of injectivity with respect to the class of all monomorphisms and with respect to some special subclasses of monomorphisms in the category Act-S of acts over a semigroup S have been studied before. In this paper, we take the category Act-S of acts over a semi...
Article
Full-text available
The actions of a semigroup or a monoid S on sets have been studied and applied in many branches of mathematics. In this paper, we generalize this notion, and introduce the category of hyper S-acts with the homomorphisms between them. Then, using the usual notion of congruences defined for hyper S-acts, quotients are defined and isomorphism theorems...
Article
Full-text available
s-dense monomorphisms and injectivity with respect to these monomorphisms were rst introduced and studied by Giuli for acts over the monoid (N ∞ , min). Ebrahimi, Mahmoudi, Moghaddasi, and Shahbaz generalized these notions to acts over a general semigroup. In this paper, we study atness with respect to the class of s-dense monomorphisms. The theory...
Book
Full-text available
Actions of a semigroup on a set have always been a useful tool to study mathematical structures, and recently have captured the interest of some computer scientists, too. For this reason and because of its close relation to the category of sets, one can take the category of S-acts, for a semigroup S, as the universe of discourse to study mathematic...
Article
Full-text available
An important notion related to injectivity with respect to monomorphisms or any other class M of morphisms in a category A is essentialness. In this paper, taking A to be the category of right acts over a semigroup S, C to be an arbitrary clo-sure operator in the category Act-S, and M d to be the class of C-dense monomorphisms resulting from a clos...
Data
Full-text available
In this paper some properties of weak regular injectiv-ity for S-posets, where S is a pomonoid, are studied. The behaviour of different kinds of weak regular injectivity with products, coprod-ucts and direct sums is considered. Also, some characterizations of pomonoids over which all S-posets are of some kind of weakly regular injective are obtaine...
Article
Full-text available
To study mathematical notions, such as injectivity with respect to the class M of (mono)morphisms in a category A, one needs to have some categorical and algebraic information about the pair (A, M). In this paper, we take A to be the category Act-S of acts over a semigroup S, C to be an arbitrary closure operator in the category Act-S, and M d to b...
Data
Full-text available
The actions of a semigroup or a monoid S on sets have been studied and applied in many branches of mathematics. In this paper, we generalize this notion, and introduce the category of hyper S-acts with the homomorphisms between them. Then, using the usual notion of congruences defined for hyper S-acts, quotients are defined and isomorphism theorems...
Conference Paper
Full-text available
In this paper the notion of down closed regular injectivity in the category Pos-S of S-posets for a pomonoid S is studied. We give some characterizations of pomonoids over which all S-posets are a weak kind of regular injectivity.
Conference Paper
Full-text available
In this paper the notion of regular injectivity in the category Pos-S of S-posets for a pomonoid S is studied. We give some characterizations of pomonoids over which all S-posets are regular injective and study the behaviour of regular (weak) injectivity with respect to products, coproducts, and direct sums.
Article
Full-text available
The class Md of sequentially dense monomorphisms were first defined and studied by Giuli, Ebrahimi, and Mahmoudi for projection algebras (acts over the monoid (N ∞ , min), of interest to computer scientists, as studied by Herrlich, Ehrig, and some others) and generalized to acts over arbitrary semigroups. Md- injectivity has been shown by some of t...
Article
Full-text available
Banaschewski defines and gives sufficient conditions on a category A and a subclass M of its monomorphisms under which M-injectivity properly behaves with respect to the notions such as M-absolute retract, M-essentialness, and the existence of M-injective hulls. In this article, taking A to be the category of acts over a semigroup S and Md to be th...
Conference Paper
Full-text available
Let M be a class of (mono)morphisms in a category A. To study mathematical notions, such as injectivity, tensor products, flatness, one needs to have some categorical and algebraic information about the pair (A,M). In this paper we take A to be the category Act-S of S-acts, for a semigroup S, and M d to be the class of sequentially dense monomor-ph...
Article
Full-text available
Sequentially dense monomorphisms and injectivity with respect to these monomorphisms were first introduced and studied by Giuli for acts over the monoid (N∞, min). In this paper we generalize these notions to acts over a general semigroup, and study the behaviour of this notion of injectivity with respect to products, coproducts, and direct sums. A...
Article
Full-text available
condition for the existence of dense injective hull in the category of Act-S. The question now is whether the converse is true in general. We show that although S 2 = S is not generally a necessary condition for the existence of dense injective hull, but in some case it is. Also, we give an explicit description of the dense injective hull, for the...
Article
Full-text available
Banaschewski defines and gives sufficient conditions on a category A and a subclass M of its monomorphisms under which M-injectivity well-behaves with respect to the notions such as M-absolute retract and M-essentialness. In this paper, taking A to be the category of acts over a semigroup S and Md to be the class of C-dense monomorphisms resulting...
Article
Full-text available
Let M be a class of (mono)morphisms in a category A. To study mathematical notions, such as injectivity, tensor products, flatness, one needs to have some categorical and algebraic information about the pair (A,M). In this paper we take A to be the category Act-S of S-acts, for a semigroup S, and M d to be the class of sequentially dense monomor-ph...

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Projects

Projects (2)
Project
Introducing the category of poset acts
Archived project