Categories and General Algebraic Structures with Applications is an international journal published by Shahid Beheshti University, Tehran, Iran, free of page charges. It publishes original high quality research papers and invited research and survey articles mainly in two subjects: Categories (algebraic, topological, and applications in mathematics and computer sciences) and General Algebraic Structures (not necessarily classical algebraic structures, but universal algebras such as algebras in categories, semigroups, their actions, automata, ordered algebraic structures,  lattices (of any kind), quasigroups, hyper universal algebras, and their applications.

Categories and General Algebraic Structures with Applications is an international journal published by Shahid Beheshti University in Tehran, Iran, with no page charges. It publishes original high-quality research papers and invited research and survey articles primarily in two areas: Categories (including algebraic, topological, and applications in mathematics and computer sciences) and General Algebraic Structures (not limited to classical algebraic structures, but also universal algebras such as algebras in categories, semigroups and their actions, automata, ordered algebraic structures, lattices of any kind, quasigroups, hyper universal algebras, and their applications).

《Categories and General Algebraic Structures with Applications》是由伊朗德黑兰的沙希德·贝赫提大学出版的国际期刊，免收版面费。该期刊主要发表高质量的原创研究论文，以及邀请的研究和综述文章，涵盖两个主要领域：范畴（包括代数、拓扑及其在数学和计算机科学中的应用）和一般代数结构（不仅限于经典代数结构，还包括如范畴中的代数、半群及其作用、自动机、有序代数结构、各种类型的格、准群、超普遍代数及其应用等）。

Categories and General Algebraic Structures with Applications

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 $(r,t)$-injectivity in the category {\bf S-Act}, where $r$ and $t$ are Hoehnke radicals, and discuss whether this kind of injectivity well-behaves.

Mahdieh Haddadi

Seyed Mojtaba Naser Sheykholislami

Categories and General Algebraic Structures with Application

(r,t)-injectivity in the category S-Act

(r,t)-内射性在S-Act范畴中的研究

K. Adaricheva and M. Bolat have recently proved that if $\,\mathcal U_0$ and $\,\mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $j\in \{0,1,2\}$ and $k\in\{0,1\}$ such that $\,\mathcal U_{1-k}$ is included in the convex hull of $\,\mathcal U_k\cup(\{A_0,A_1, A_2\}\setminus\{A_j\})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ for the more general case where $\,\mathcal U_0$ and $\,\mathcal U_1$ are compact sets in the plane such that $\,\mathcal U_1$ is obtained from $\,\mathcal U_0$ by a positive homothety or by a translation. Also, we give a short survey to show how lattice theoretical antecedents, including a series of papers on planar semimodular lattices by G. Grätzer and E. Knapp, lead to our result.

Gábor Czédli

Árpád Kurusa

A convex combinatorial property of compact sets in the plane and its roots in lattice theory

平面中紧集的凸组合性质及其在格论中的根源

In this paper, first we introduce the notions of an $(m,n)$-hyperideal and a generalized $(m,n)$-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize $(m,n)$-regularity, $(m,0)$-regularity, and $(0,n)$-regularity of an ordered semihypergroup in terms of its $(m,n)$-hyperideals, $(m,0)$-hyperideals and $(0,n)$-hyperideals, respectively. The relations ${_m\mathcal{I}}, \mathcal{I}_n, \mathcal{H}_m^n$, and $\mathcal{B}_m^n$ on an ordered semihypergroup are, then, introduced. We prove that $\mathcal{B}_m^n \subseteq \mathcal{H}_m^n$ on an ordered semihypergroup and provide a condition under which equality holds in the above inclusion. We also show that the $(m,0)$-regularity [$(0,n)$-regularity] of an element induce the $(m,0)$-regularity [$(0,n)$-regularity] of the whole $\mathcal{H}_m^n$-class containing that element as well as the fact that $(m,n)$-regularity and $(m,n)$-right weakly regularity of an element induce the $(m,n)$-regularity and $(m,n)$-right weakly regularity of the whole $\mathcal{B}_m^n$-class and $\mathcal{H}_m^n$-class containing that element, respectively.

Ahsan Mahboob

Noor Mohammad Khan

Bijan Davvaz

(m,n)-Hyperideals in Ordered Semihypergroups

有序半超群中的(m,n)-超理想

Condition $(PWP)$ which was introduced in (Laan, V., {\it Pullbacks and flatness properties of acts I}, Commun. Algebra, 29(2) (2001), 829-850), is related to flatness concept of acts over monoids. Golchin and Mohammadzadeh in ({\it On Condition $(PWP_E)$}, Southeast Asian Bull. Math., 33 (2009), 245-256) introduced Condition $(PWP_E)$, such that Condition $(PWP)$ implies it, that is, Condition $(PWP_E)$ is a generalization of Condition $(PWP)$. In this paper we introduce Condition $(PWP_{ssc})$, which is much easier to check than Conditions $(PWP)$ and $(PWP_E)$ and does not imply them. Also principally weakly flat is a generalization of this condition. At first, general properties of Condition $(PWP_{ssc})$ will be given. Finally a classification of monoids will be given for which all (cyclic, monocyclic) acts satisfy Condition $(PWP_{ssc})$ and also a classification of monoids $S$ will be given for which all right $S$-acts satisfying some other flatness properties have Condition $(PWP_{ssc})$.

Pouyan Khamechi

Hossein Mohammadzadeh Saany

Leila Nouri

Classification of monoids by Condition $(PWP_{ssc})$

通过条件 $(PWP_{ssc})$ 对幺半群进行分类

We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar\'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of the D-topological structure. We also study quasi-cosheaves, defined by pre-cosheaves which respect the colimit over covering generating families, and prove that cosheaves are quasi-cosheaves. Finally, a so-called quasi-\v{C}ech homology with values in pre-cosheaves is established for diffeological spaces.

Alireza Alireza Ahmadi

Akbar Dehghan Nezhad

Some aspects of cosheaves on diffeological spaces

微分流形空间上余层的若干方面

In this paper we show that the prime saturated prefilter monads are sup-dense and interpolating in saturated prefilter monads. It follows that CNS spaces are the lax algebras for prime saturated prefilter monads. As for the algebraic part, we prove that the Eilenberg-Moore algebras for saturated prefilter monads are exactly continuous I-lattices.

Gao Zhang

Wei He

On saturated prefilter monads

关于饱和预滤子单子

The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized to Q-categories by Kostanek and Waszkiewicz, where Q is a commutative and unital quantale. This paper concerns the influence of the structure of the quantale Q on the connection between Yoneda completeness of Q-categories and directed completeness of their sets of formal balls. In the case that Q is the unit interval [0, 1] equipped with a continuous t-norm &, it is shown that in order that Yoneda completeness of each Q-category be equivalent to directed completeness of its set of formal balls, a necessary and sufficient condition is that the t-norm & is Archimedean.

Xianbo Yang

Dexue Zhang

Formal balls of Q-categories

Q-范畴的正则球

One of the aims of the modern representation theory is to solve classification problems for subcategories of modules over a unitary ring R. In this paper, we introduce the concept of 1-absorbing comultiplication modules and classify 1-absorbing comultiplication modules over local Dedekind domains and we study it in detail from the classification problem point of view. The main purpose of this article is to classify all those indecomposable 1-absorbing comultiplication modules with finite-dimensional top over pullback rings of two local Dedekind domains and establish a connection between the 1-absorbing comultiplication modules and the pure-injective modules over such rings. In fact, we extend the definition and results given in [17] to a more general 1-absorbing comultiplication modules case.

Farkhondeh Farzalipour

Peyman Ghiasvand

Classification of 1-absorbing comultiplication modules over a pullback ring

拉回环上1-吸收余乘法模的分类

The aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice $\mathcal{SI}(L)$ of a state residuated lattice $(L, \varphi)$ and prove that it is a complete Brouwerian lattice in which the meet and the join of any two compact elements are compact (coherent frame). We characterize the notion of prime state ideals in SRLs. In addition, we establish the condition for which the lattice $\mathcal{SI}(L)$ is a Boolean algebra.

短名
Journal Impact	0.75
国际分区	MATHEMATICS(Q3)

涉及主题	数学纯数学组合数学离散数学计算机科学哲学数学分析物理域代数上的认识论几何学量子力学程序设计语言语言学人工智能化学生物
出版信息	出版商: Shahid Beheshti University，出版周期: ，期刊类型: journal，开源期刊: 是
基本数据	创刊年份: 2017，原创研究文献占比: 100.00%，自引率:0.00%， Gold OA占比: 41.03%
平均审稿周期	网友分享经验：8 Weeks

Categories and General Algebraic Structures with Applications

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