Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585325120260701Bounded complexes of objects of finite flat dimensions10548910.48308/cgasa.2024.184656.1499ENEsmaeilHosseiniDepartment of Mathematics, Faculty of Mathematics and Computer Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran.Kiana K.IzadyarDepartment of Mathematics, Faculty of Mathematics and Computer Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran.Journal Article20240612Let $(\mathcal{R},\otimes)$ be a symmetric monoidal closed Grothendieck category which has enough flat objects. It is shown that a given object ${\mathcal{G}}$ in $\mathcal{R}$ has finite flat dimension if and only if it is quasi-isomorphic to a bounded complex of objects of finite flat dimension. In the case in which $\mathcal{R}$ has enough projective objects, we prove that finite flat dimension in $\mathcal{R}$ implies finite projective dimension if and only if any object in $\mathcal{R}$ that is quasi-isomorphic to a bounded complex of objects of finite flat dimension has finite projective dimension. This leads to a generalization of [4, Proposition 2.3] and [15, Theorem]. Moreover, we present a wide class of $n$-perfect rings.https://cgasa.sbu.ac.ir/article_105489_e0cac705fe54337f275f742fecfa613b.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585325120260701A note on the first nonzero Fitting ideal of a module10616910.48308/cgasa.2025.236826.1518ENSomayehHadjirezaeiDepartment of Mathematics,
Vali-e-Asr University of Rafsanjan, Iran0000-0002-8994-5523Journal Article20240907Let $R$ be a commutative ring and $M$ be a finitely generated $R$-module. Let I$(M)$ be the first nonzero Fitting ideal of $M$. In this paper we characterize some modules over Noetherian UFDs, whose first nonzero Fitting ideal is a prime ideal. We show that if $P$ is a prime ideal and $M$ is a finitely generated R-module with I$(M) = P$ and T$(M_P)\neq 0$, then M is isomorphic to $R/P \oplus N$, for some projective R-module $N$ of constant rank. Also, we investigate some conditions under which ${M}/$T$(M)$ is free.https://cgasa.sbu.ac.ir/article_106169_4fbb34893d933629fe7d7e31ed3d7cc0.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585325120260701Exploring new upper and lower bounds for the $A_{\alpha}$-energy of graphs10706210.48308/cgasa.2026.242533.1585ENMainakBasuniaDepartment of Mathematics, Indian Institute of Technology Kharagpur, IndiaPratimaPanigrahiDepartment of Mathematics, Indian Institute of Technology Kharagpur, IndiaJournal Article20251117Let $G$ be a graph on $n$ vertices and $m$ edges. For $\alpha \in [0,1]$, the $A_{\alpha}$-matrix of $G$ is defined as $A_{\alpha}(G) = \alpha D(G) + (1- \alpha) A(G)$, where $A(G)$ is the adjacency matrix and $D(G)$ is the degree diagonal matrix of $G$. If $\rho_1 \geq \rho_2 \ldots \geq \rho_n$ are the eigenvalues of $A_{\alpha}(G)$, the $A_{\alpha}$-energy of $G$ is defined as $E_{A_{\alpha}}(G) = \sum_{i=1}^{n} |\rho_i -\frac{2\alpha m}{n}|$. In this paper, we present novel upper and lower bounds for $E_{A_\alpha}(G)$ in terms of standard graph invariants, showing that each bound is sharp and identifying the specific graphs attaining them. For selected bounds, we provide brief comparative analysis with existing results, observing improved estimates. Furthermore, we establish new relations between $E_{A_\alpha}(G)$ and other well known graph energies, including adjacency, Laplacian, as well as the adjacency energy of the line graph.https://cgasa.sbu.ac.ir/article_107062_9f47c6429548a3dfe3fa5321692900b9.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585325120260701The spectrum of $\sigma$-frames in the adjunction between $\sigma$-frames and $\sigma$-spaces10698410.48308/cgasa.2026.241071.1565ENZohrehMaghsoudloo NejadDepartment of Mathematics, Go.C., Islamic Azad University, Gorgan, Iran.AbolghasemKarimi FeizabadiDepartment of Mathematics, Go.C., Islamic Azad University, Gorgan, Iran.0000-0002-5659-8262HosseinZahmatkeshDepartment of Mathematics, Go.C., Islamic Azad University, Gorgan, Iran.AhmadHaghbinDepartment of Mathematics, Go.C., Islamic Azad University, Gorgan, Iran.Journal Article20250811In this paper, we define an adjunction between two categories: $\sigma$-frames and $\sigma$-spaces, denoted by the pair $(\Sigma^\sigma, \Lambda)$. The functor $\Sigma^\sigma$ is constructed using the concept of $\sigma$-points. We prove that $\sigma$-points are equivalent to $\sigma$-completely prime filters, but unlike in pointfree topology, they do not correspond to prime elements. While every prime element determines a corresponding $\sigma$-point, the converse fails. For $\sigma$-frames, we define the $\sigma$-spatiality condition, which is equivalent to having enough $\sigma$-points. Dually, for $\sigma$-spaces, the $\sigma$-soberness condition is shown to be equivalent to the conjunction of the $\sigma_0$ separation axiom and $\sigma$-pointedness properties. These conditions naturally emerge from careful analysis of the adjunction morphisms.https://cgasa.sbu.ac.ir/article_106984_db4f7695d3dc40726311747633e3fca6.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585325120260701When Freudenthal coincides with the smallest compactification with a categorical slant10696810.48308/cgasa.2024.234534.1468ENSimo SMthethwaDisciplines of Mathematics, School of Agriculture and Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa0000-0003-1809-5899GugulethuNogwebelaDisciplines of Mathematics, School of Agriculture and Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South AfricaJournal Article20240121In this note, for a certain class of regular continuous frames, we establish conditions that are equivalent to saying that the Freudenthal compactification and the smallest compactification are indistinguishable; in turn, this expands the list of conditions under which the smallest compactification is perfect, which is available in the literature. We define a new class of morphisms between frames, called <em>F</em>-maps, and provide a proof demonstrating that the category of compact regular frames and <em>F</em>-maps forms a coreflective full subcategory of the category of rim-compact frames and <em>F</em>-maps. This coreflection is evidenced by the join map associated with the Freudenthal compactification. Accordingly, this provides an affirmative answer to the question by Herrlich, which inquired whether the Freudenthal compactification can be regarded as a reflection with "sensible" maps.https://cgasa.sbu.ac.ir/article_106968_77c49dcdb7b4cc58e5b07267c2df8908.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585325120260701Nucleus topology in equality algebras10696710.48308/cgasa.2026.243407.1601ENSogolNiazianFaculty of Medicine, Tehran Medical Sciences, Islamic Azad University, Tehran, IranRajab AliBorzooeiDepartment of Mathematics, Faculty of Mathematical Sciences,
Shahid Beheshti University, Tehran, IranMonaAaly KologaniHatef Higher Education Institute, Zahedan, Iran0000-0002-5234-2876Journal Article20260203In this paper, we define the concept of nucleus map on equality algebras and study related results. Then, using this concept and upsets, a topology on equality algebras is constructed and it is shown that the equality algebra with this topology becomes a topological space. In addition, some properties of topological space such as compactness and connectedness are investigated. Moreover, we study the continuity of all operations with respect to the topology on equality algebras. <br>Finally, the relations between the two topologies in quotient equality algebras are revealed.https://cgasa.sbu.ac.ir/article_106967_b43aadb7a6768920486ff2a7302d7901.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585325120260701Characterization of Monoids by Condition $(PWP_{S})$ of right acts10581310.48308/cgasa.2025.236800.1517ENHosseinMohammadzadeh SaanyDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.ZohreKhakiDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.Journal Article20240904In [8] Valdis Laan introduced Condition (PW P). Golchin and Mohammadzadeh in [3] introduced Condition (PW P_E), such that Condition (PW P) implies it but the converse is not true in general. In this paper at first we introduce a generalization of Condition (PW P_E), called Condition (PW P_S). Then will give some general properties and a characterization of monoids for which all right acts satisfy this condition. Also, we give a characterization of monoids, by comparing this property of their acts with some others. Finally, we will give a characterization of monoid S, for which S^{I}_{S}, for any non-empty set I and S^{S \times S}_{S}, satisfy Condition(PW P_S).https://cgasa.sbu.ac.ir/article_105813_38f1a9864669a6d5eb095bf14f420938.pdfShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585325120250924The dual-classical Krull dimension of rings via topology10625110.48308/cgasa.2025.238090.1531ENNasrinShiraliDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran0000-0002-9907-7352Sayed MalekJavdannezhadDepartment of Science, Shahid Rajaee Teacher Training University: Tehran, Tehran, IranJournal Article20241227Let $R$ be a ring and $\mathcal{X} = \mathcal{SH}(R)-\{0\}$ be the set all of non-zero strongly hollow ideals (briefly, $sh$-ideals) of $R$. We first study the concept $SH$-topology and investigate some of the basic properties of a topological space with this topology. It is shown that, if $\mathcal X $ is with $SH$-topology, then $\mathcal {X}$ is Noetherian if and only if every subset of $\mathcal X$ is quasi-compact if and only if $R$ has $dcc$ on semi-$sh$-ideals. Finally, the relation between the dual-classical Krull dimension of $R$ and the derived dimension of $\mathcal {X}$ with a certain topology has been studied. It is proved that, if $\mathcal {X}$ has derived dimension, then $R$ has the dual-classical Krull dimension and in case $R$ is a $D$-ring (i.e., the lattice of ideals of $R$ is distributive), then the converse is true. Moreover these two dimension differ by at most $1$.https://cgasa.sbu.ac.ir/article_106251_b2e1a832a852780f31d0640a908b6af9.pdf