https://jas.shahroodut.ac.ir/ Journal of Algebraic Systems en daily 1 Wed, 01 Apr 2026 00:00:00 +0430 Wed, 01 Apr 2026 00:00:00 +0430 https://jas.shahroodut.ac.ir/article_3731.html Let $X$ be a mixed graph and $\omega=\frac{1+\i \sqrt{3}}{2}$. We write $i\rightarrow j$, if there is an oriented edge from a vertex $v_i$ to another vertex $v_j$, and $i\sim j$ for an un-oriented edge between the vertices $v_i$ and $v_j$. The degree of a vertex $v_i$ is denoted by $d_i$. We propose the Hermitian Randi\'c matrix of second kind $R^\omega(X)\coloneqq(R^\omega_{ij})$, where $R^\omega_{ij}=\frac{1}{\sqrt{d_id_j}}$ if $i \sim j$, $R^\omega_{ij}= \frac{\omega}{\sqrt{d_id_j}}$ and $R^\omega_{ji}= \frac{\overline{\omega}}{\sqrt{d_id_j}}$ if $i\rightarrow j$, and 0 otherwise. In this paper, we investigate some spectral features of this novel Hermitian matrix and study a few properties like positiveness, bipartiteness, edge-interlacing etc. We also compute the characteristic polynomial for this new matrix and obtain some upper and lower bounds for the eigenvalues and the energy of this matrix. https://jas.shahroodut.ac.ir/article_3732.html The goal of this study is to provide an innovation for commutativity research that is less than the strong condition prime ring. This paper will describe weakly right cancellative semirings and examine how commutativity and generalized derivations apply to this class of semirings. A detailed explanation and classification of some of these generalized derivations are also included. https://jas.shahroodut.ac.ir/article_3733.html We compute spectrum, energy, Laplacian spectrum/ energy and signless Laplacian spectrum/energy of non-commuting graphs of certain finite non-commutative rings. In particular, we consider finite rings $R$ such that $|R| = p^2, p^3, p^4$, $p^5$, $p^2q$ and $p^3q$, where $p$ and $q$ are primes. Further, we consider $n$-centralizer finite\\ rings for $n \, = \,4, \, 5$ \, and \, $p \,+ \,2$; \, more generally, finite rings with central quotients isomorphic to $\mathbb{Z}_p \times \mathbb{Z}_p$. Our computations reveal that non-commuting graphs of these rings are L-integral. We also determine whether non-commuting graphs of these rings are integral, Q-integral, hyperenergetic, L-hyperenergetic or Q-hyperenergetic. https://jas.shahroodut.ac.ir/article_3734.html In this paper, we apply the concepts of intuitionistic fuzzy translations and intuitionistic fuzzy multiplications of intuitionistic fuzzy sets to the PMS-subalgebras of a PMS algebra and investigate several related results. The relationships between intuitionistic fuzzy PMS-subalgebras of a PMS-algebra and intuitionistic fuzzy ω-translations, and intuitionistic fuzzy ζ-multiplications of intuitionistic fuzzy PMS-subalgebras are discussed. Finally, we discuss the ideas of intuitionistic fuzzy magnified ζω - translations of intuitionistic fuzzy PMS-subalgebras of a PMS-algebra and investigate some associated results. https://jas.shahroodut.ac.ir/article_3735.html Suppose that $\ab$ is an ideal of a given commutative Noetherian ring $R$ such that the $R$-modules $H^1_{\ab}(M)$ and $H^3_{\ab}(M)$ are $\ab$-cofinite, for every finitely generated $R$-modules $M$. In this paper, it is shown that the $R$-modules $H^i_{\ab}(M)$ are $\ab$-cofinite, for all finitely generated $R$-modules $M$ and all integers $i\in\Bbb{N}_0$. https://jas.shahroodut.ac.ir/article_3736.html Recently, a construction of minimal codes arising from a family of almost Ramanujan graphs was shown. Ramanujan graphs are examples of expander graphs that minimize the second-largest eigenvalue of their adjacency matrix. We call such graphs Ramanujan, since all known non-trivial constructions imply the Ramanujan conjecture on arithmetical functions. In this paper, we prove that some families of tangent graphs of finite classical polar spaces satisfy Ramanujan's condition. If the polarity is unitary, or it is orthogonal and the quadric is over the binary field, the tangent graphs are strongly regular, and we know their spectrum. By direct computation, it is possible to show which families of tangent graphs are Ramanujan. https://jas.shahroodut.ac.ir/article_3737.html In this paper, we characterize the capability of nilpotent n- Lie algebras of dimensionat most n + 3 over an arbitrary field when n > 2$ and the capability of 7 -dimensional nilpotent 3 -Lie algebras over field $\mathcal {K} $ with $char \mathcal {K}\ ne 2$. https://jas.shahroodut.ac.ir/article_3738.html The notion of K-frames generalizes ordinary frames in that the lower frame bound applies only to elements within the range of K. This paper will introduce the new concept of K-bi-g-frames for Hilbert spaces. Then, we examine some characterizations with the help of a biframe operator. Finally, we investigate several results about the stability of K-bi-g-frames produced using frame theory methods. https://jas.shahroodut.ac.ir/article_3739.html The property of having infinitely many prime numbers award these numbers to have many applications in various fields of sciences. One of the most important applications is their use in the creation of many public key cryptosystems' private keys. Therefore, the main aim of this paper is considering a well known form of primes generated by the Fermat-Euler equation $p=x^2+dy^2$ and studying whether or not this form keeps the property of generating infinitely many primes if the unknowns $x$, $y$ and $p$ are terms in certain binary recurrence sequences called the Lucas sequences of the first kind $\{u_n(a,b)\}$ or the second kind $\{v_n(a,b)\}$. In other words, in this paper we present a technique for investigating the integer solutions $(x,y,p)$ of the equation $p=x^2+dy^2$, where the unknowns are terms in $\{u_n(a,b)\}$ or $\{v_n(a,b)\}$. We also apply this technique for determining the solutions $(x,y,p)=(t_i(a,b),t_j(a,b),t_k(a,b))$ with $1 \leq i \leq j \leq k$, where $t_n(a,b)$ represents the general term $u_n(a,b)$ or $v_n(a,b)$ under certain conditions on the integers $a$ and $b$. https://jas.shahroodut.ac.ir/article_3740.html For an ordered $k$-partition $\Omega = \{S_1, S_2, ..., S_k\}$ of vertex set of a connected graph $G$ and a vertex $v$ of $G$, the representation of $v$ with respect to $\Omega$ is defined as the $k$-tuple $r(v |\Omega) = (d(v, S_1), d(v, S_2), ..., d(v, S_k )).$ The partition $\Omega$ is called a resolving partition of $G$, if $r(u|\Omega)\neq r(v|\Omega)$ for all distinct $u, v \in V(G)$. The partition dimension of a graph $G$, denoted by $pd(G)$, is the cardinality of a minimum resolving partition of $G$. A subset $D\subseteq V(G)$ is $k$-dominating in $G$, if every vertex of $V(G)\setminus D$ has at least $k$ neighbors in $D$. The minimum cardinality among all $k$-dominating sets is called the $k$-domination number of $G$, denoted by $\gamma_k(G)$. In this paper, we determine the partition dimension of cocktail party graph $CP(m+1)$ and corona product $G\circ\overline{K_m}$. Moreover, we obtain $k$-domination numbers for $CP(m+1)$ and corona product $C_n\circ\overline{K_m}$. https://jas.shahroodut.ac.ir/article_3741.html In (Categories and General AlgebraicStructures with Applications, 12(1):175-197 (2020)), Rashidi et al. introduced GPW-flatnessof acts over monoids as a generalization of principalweak flatness.In this paper, we introduce Condition (GPWPsec) of acts overmonoids and compare it with GPW-flatness. Also, we obtainsome general properties of Condition (GPWPsec) and characterize those monoids for which this condition implies some otherproperties and vice versa.در( رسته ها و ساختارهای جبری عمومی با کاربردها 12(1):175-197(2020))، رشیدی و همکاران خاصیتهمواری - GPWسیستم ها روی تکواره ها را به عنوان تعمیمی از به طور اساسی ضعیف همواری معرفی کردند. در این مقاله شرط (〖GPWP〗_sec)از سیستم ها روی تکواره ها را ارائه و آن را با همواری - GPWمقایسه می کنیم. همچنین برخی از خواص کلی شرط (〖GPWP〗_sec). را به دست می آوریم و به دسته بندی تکوارهایی خواهیم پرداخت که این شرط سایر خواص را نتیجه دهد و برعکس https://jas.shahroodut.ac.ir/article_3742.html Let $R$ be a commutative ring with identity. For $t\in N$, a proper submodule $N$ of an $R$-module $M$ is called a t-prime submodule if $rm\in N~(r\in R, m\in M)$, then $m\in N$ or $r^t\in (N:_RM)$. We obtain some other characterizations of t-prime submodules. Also by some other notions like t-secondary submodules, various properties of t-prime submodules are investigated. To this end, we deal with irreducible as well as reduced t-prime decompositions of a submodule. We provide several examples with illustrate our results.