Mahdieh Haddadi

Mahdieh Haddadi
Semnan University · Faculty of Mathematics, Statistics and Computer Science

PhD

About

23
Publications
968
Reads
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40
Citations
Citations since 2016
12 Research Items
27 Citations
201620172018201920202021202201234567
201620172018201920202021202201234567
201620172018201920202021202201234567
201620172018201920202021202201234567
Additional affiliations
September 2010 - March 2011
Technische Universität Braunschweig
Position
  • Exchange reseacher
January 2009 - October 2011
Shahid Beheshti University
Position
  • Lecturer

Publications

Publications (23)
Article
Graph theory is a useful tool to study the properties of algebraic structures. Here we are going to employ this tool to study nominal sets. To do so, we employ the freshness relation to construct certain graphs so-called fresh-graph, due to the key role of freshness relation in obtaining these graphs. We then investigate the properties of these gra...
Article
Full-text available
In this paper, we show that injectivity with respect to the class D of dense monomorphisms of an idempotent and weakly hereditary closure operator of an arbitrary category well-behaves. Indeed, if M is a subclass of monomorphisms, M ∩ D-injectivity well-behaves. We also introduce the notion of (r, t)-injectivity in the category S-Act, where r and t...
Article
In this paper, we show that injectivity with respect to the class $\mathcal{D}$ of dense monomorphisms of an idempotent and weakly hereditary closure operator of an arbitrary category well-behaves. Indeed, if $\mathcal{M}$ is a subclass of monomorphisms, $\mathcal{M}\cap \mathcal{D}$-injectivity well-behaves. We also introduce the notion of $(r,t)$...
Preprint
Full-text available
Various generalizations of the concept of injectivy, in particular injectivy with respect to a specific class of morphisms, have been intensively studied throughout the years in different categories. One of the important kinds of injectivy studied in the category R-Mod of R-modules is ${\tau}$-injectivy, for a torsion theory ${\tau}$, or in the oth...
Preprint
Full-text available
In abelian categories like the category of R-modules and even in the category S-Act 0 of S-acts with a unique zero, idempotent radicals and torsion theories are equivalent, and the {\tau}-torsion and {\tau}- torsion free classes of a torsion theory {\tau} are closed under coproducts. These are not necessarily true in the category S-Act of S-acts. I...
Article
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Let S-Set be the category of S-sets, sets together with the actions of a semigroup S on them. And, let S-Pos be the category of S-posets, posets together with the actions compatible with the orders on them. In this paper we show that the category S-Pos is a radical extension of S-Set; that is there is a radical on the category S-Pos, the order deso...
Article
In this paper we investigate the actions of a monoid of the form S = G∪I, where G is a group and I is an ideal of S, on sets. So, naturally, every S-act can be considered as an I¹-act. The central question here is that what is the relation between injective and weakly injective I¹-acts and injective and weakly injective S-acts? We are going to resp...
Article
The study of monoids in the category of monoid acts leads to the notion of power action. In this paper, for a monoid T, we investigate the relationship between the category T-Act of all T-acts and the category T-Pwr of all T-power acts. For a T-power act M on a commutative monoid T, we introduce the covariant functor MM- from T-Act to T-Pwr and sho...
Article
Full-text available
The notion of a Cauchy sequence in an S-poset is a useful tool to study algebraic concepts, specially the concept of injectivity. This paper is concerned with the relations between injectivity and Cauchy sequences in the category of S-posets in which S is a left zero posemi- group. We characterize subdirectly irreducible S-posets over this posemigr...
Article
Full-text available
Although fuzzy set theory and sheaf theory have been developed and studied independently, Ulrich Hohle shows that a large part of fuzzy set theory is in fact a subfield of sheaf theory. Many authors have studied math- ematical structures, in particular, algebraic structures, in both categories of these generalized (multi)sets. Using Hohle's idea, w...
Article
Full-text available
An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is proved to be the free corecursive monad, where the co...
Article
Some of the so called smallness conditions in algebra as well as in category theory, are important and interesting for their own and also tightly related to injectivity, are essential boundedness, cogenerating set, and residual smallness. In this overview paper, we �rst try to refresh these smallness condition by giving the detailed proofs of the r...
Article
Full-text available
Abstract. Some of the so called smallness conditions in algebra as well as in category theory, are important and interesting for their own and also tightly related to injectivity, are essential boundedness, cogenerating set, and residual smallness. In this overview paper, we �rst try to refresh these smallness condition by giving the detailed proof...
Article
Full-text available
Sequentially dense monomorphisms were first introduced and studied by Giuli for projection algebras and followed by Ebrahimi, Mahmoudi, Moghaddasi and Shahbaz for S-acts. In this paper we use the notion of sub-Cauchy sequences and introduce the class of regular sub-sequentially dense monomorphisms for S-posets, denoted by Ms. We investigate the pro...
Article
Full-text available
Abstract. Nets, useful topological tools, used to generalize certain concepts that may only be general enough in the context of metric spaces. In this work we introduce this concept in an S-poset, a poset with an action of a posemigroup S on it which is a very useful structure in computer sciences and interesting for mathematicians, and give the co...
Article
Full-text available
Purity and equational compactness play a role at least in the Theories of Modules, Acts, Model, and Category. Adámek and Rosický have studied them categorically, Rothmaler model-theoretically, and some authors, including Banaschewski, Gould, and Normak have studied these notions on G-acts. We take both the group G and the set A in the definition of...
Conference Paper
Full-text available
An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as a coproduct of the final coalgebra (considered as an algebra) and with free algebras. The monad of free corecursive algebras is proved to be the free corecursive monad, where the...
Article
Full-text available
Nowadays purity plays a role in at least four branches of mathematics: Module Theory, Theory of Acts over semigroups, Model Theory, and Category Theory. Adámek and Rosciký have studied these notions categorically, and Rothmaler model-theoretically. Some authors including Banaschewski, Gould, and Normak have studied purity on G-acts, acts over a mon...

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Projects (5)