Mojtaba Sedaghatjoo

Mojtaba Sedaghatjoo
Persian Gulf University | PGU · Department of Mathematics

PhD

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11
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Publications

Publications (11)
Article
A theorem in the paper ”Characterization of Monoids by Properties of Generators”, written by Kilp and Knauer, states that amalgamated coproducts of generators are generators in the category Act-S of right S-acts over a monoid S. In this note we give a counterexample to deny this theorem. However we show that the results in that paper based on the m...
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The paper is devoted to the investigation of uniform notion for acts over semigroups perceived as an overclass of subdirectly irreducible acts. We establish conditions to fill the gap between these classes of acts. Besides we prove that uniform acts with two zeros are subdirectly irreducible. Ultimately we investigate monoids which are uniform as r...
Article
This paper is devoted to the preservation of injective properties under limits and their transfer from colimits to the components. We prove that an injective property α is preserved under limits if and only if all acts satisfy property α. Besides we prove that an injective property α is transferred from colimits to their components if and only if a...
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Themainpurposeofthispaperistoinvestigateclassesofactsthatareinjective relative to all embeddings with indecomposable domains or codomains. We give some homological classifcations of monoids in light of such kinds of injectivity. Our approach to the indecomposability property provides a new characterization of right absolutely injective monoids such...
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In this paper we prove that for a monoid $S$, products of indecomposable right $S$-acts are indecomposable if and only if $S$ contains a right zero. Besides, we prove that subacts of indecomposable right $S$-acts are indecomposable if and only if $S$ is left reversible. Ultimately, we prove that the one element right $S$-act $\Theta_S$ is product f...
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This paper is devoted to the study of products of classes of right S-posets possessing one of the flatness properties and preservation of such properties under products. Specially, we characterize a pomonoid S over which its nonempty products as right S-posets satisfy some known flatness properties. Generalizing this results, we investigate product...
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This paper addresses conditions under which all generators in the category of right S-acts (where S is a monoid) satisfy a flatness property. There are charac-terizations for monoids over which all generators satisfy a flatness property α where α can stand for freeness, projectivity, strong flatness, Condition (P), principal weak flatness and torsi...
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If S is a monoid, the set S×S equipped with componentwise S-action is called the diagonal act of S and is denoted by D(S). We prove the following theorem: the right S-act S n (1≠n∈ℕ) is (principally) weakly flat if and only if Õi=1nAi\prod _{i=1}^{n}A_{i} is (principally) weakly flat where A i ,1≤i≤n are (principally) weakly flat right S-acts, if...
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For a monoid S, the set S × S equipped with the componentwise right S-action is called the diagonal act of S and is denoted by DDSS. A monoid S is a left PP (left PSF) monoid if every principal left ideal of S is projective (strongly flat). We shall call a monoid S left PPPP if all principal left ideals of S satisfy condition (P). We shall call a m...
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In this article we characterize monoids over which every right S-act has a strongly flat (condition (P)) cover. Similar to the perfect monoids, such monoids are characterized by condition (A) and having strongly flat (condition (P)) cover for each cyclic right S-act. We also give a new characterization for perfect monoids as monoids over which ever...
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We shall call a monoid S principally weakly (weakly) left coherent if direct products of nonempty families of principally weakly (weakly) flat right S-acts are principally weakly (weakly) flat. Such monoids have not been studied in general. However, Bulman-Fleming and McDowell proved that a commutative monoid S is (weakly) coherent if and only if t...

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Projects (2)
Project
ISEDS at Persian Gulf University (PGU) has pioneered many of the tools and ideas behind the research and applications often classified as "intelligent systems" and “data science,” where computer science, electrical engineering, statistics, and mathematics join together. This Faculty sees an even brighter future for data science as it harnesses a wider set of ideas to build a new more subtle and powerful science of data. As well as being interested in prediction and statistical computation, our Faculty puts equal weight on designing experiments, modeling sophisticated dependencies (networks, data streams), and trying to understand and quantify causal mechanisms, not simply averages and associations, with large data sets. These views are reflected in our curriculum targeted to data science specialists, our faculty’s research, and the work of our research students.
Project
The department of mathematics the Persian Gulf University (PGU), Bushehr, IRAN, is proud to host the 27-th Iranian algebra seminar Online. Date: 9-10 March 2022. Country: IRAN. City: Bushher-Online. https://ias27.pgu.ac.ir/?lang=en This seminar will be held in cooperation with members of the department of mathematics.