# Leila ShahbazUniversity of Maragheh · Department of Mathematics

Leila Shahbaz

Associate Professor

Head of Department of Mathematics

## About

28

Publications

2,109

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70

Citations

Citations since 2016

Introduction

I am working on fuzzy S-posets.

Additional affiliations

September 2008 - November 2015

October 2004 - September 2008

## Publications

Publications (28)

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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.

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...

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...

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...

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...

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...

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...

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...

## Projects

Projects (2)