Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...

is a module over the ring of all modular forms with respect to the group Γ2[4, 8]. We are interested in its structure. By Igusa, the ring of modular forms is generated by the ten classical theta constants θ[m]. The module M contains a submodule N which is generated by 45 Cohen-Rankin brackets {θ[m], θ[n]}. We determine defining relations for this submodule and compute its Hilbert function (Theo...

Mediator is a modular multiprotein complex required for regulated transcription by RNA polymerase (Pol) II. Here, we show that the middle module of the Mediator core contains a submodule of unique structure and function that comprises the N-terminal part of subunit Med7 (Med7N) and the highly conserved subunit Med31 (Soh1). The Med7N/31 submodule shows a conserved novel fold, with two proline-r...

Let R be a commutative ring with unity. And let E unitary R-module. This paper introduces the notion of 2-prime submodules as generalized concept ideal, where proper submodule H module F over is said to if , for r and x implies that or . we prove many properties this kind submodules, then only [N ] E, R. Also, non-zero multiplication module, [K: F] [H: every k such K. Furthermore, will study ba...

Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ non-negative integer. $M$ $N$ two finitely generated $R$-modules. In certain cases, we give some bounds under inclusion for the annihilators $\operatorname{Ext}^t_R(M, N)$ $\operatorname{H}^t_{\mathfrak a}(M)$ in terms minimal primary decomposition zero submodule which are independent choice decomposition. Then, by using...

The concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies this it is relationship to previous generalizationsm especially 2-Absorbing submodule submodule, addition studying most important Propositions, charactarizations Examples. Now research, which considered a continuation definition tha...

Let $G$ be a graph with eigenvalues $lambda_1(G)geqcdotsgeqlambda_n(G)$. In this paper we find all simple graphs $G$ such that $G$ has at most twelve vertices and $G$ has exactly two non-negative eigenvalues. In other words we find all graphs $G$ on $n$ vertices such that $nleq12$ and $lambda_1(G)geq0$, $lambda_2(G)geq0$ and $lambda_3(G)0$, $lambda_2(G)>0$ and $lambda_3(G)

We propose an algebraic setup for end-to-end physical-layer network coding based on submodule transmission. We introduce a distance function between modules, describe how it relates to information loss and errors, and show how to compute it. Then we propose a definition of submodule error-correcting code, and investigate bounds and constructions for such codes. Introduction and motivation In th...