Let %‘A be the category of finite dimensional right modules for a quasi-hereditary algebra A. In the context of various types of Kazhdan-Lusztig theories, we study both the homological dual A! = Extt, (A/ rad(A), A/ rad(A)) and the graded algebra grA = @rad(A)j/rad(A)j+‘. For example, we investigate a condition introduced in [6], and here called (SKL’), which guarantees that A!’ E gr A. A stren...

Abstract In this study, inspired by the definition and a previous study [F. Eryılmaz, SS-lifting modules rings , Miskolc Math. Notes 22 (2021), no. 2, 655–662], left Harada are adapted to ss-Harada rings, important properties of these provided. The characterization ring R R with perfect Rad</...

LetG be a finite p-group,K a field of characteristic p, and J the radical of the group algebra K[G]. We study modular representations using some new results of the theory of extensions of modules. More precisely, we describe the K[G]-modules M such that J2M = 0 and give some properties and isomorphism invariants which allow us to compute the number of isomorphism classes of K[G]-modulesM such t...

It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if RR (or RR) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie d...

Let L be a lattice with the greatest element 1. Following concept of Radsupplemented modules, we define Rad-supplemented filters and will make an intensive investigate basic properties possible structures these filters.

All rings are commutative with 1 6= 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an R-module M is called a 2-absorbing primary submodule of M if whenever a, b ∈ R and m ∈M and abm ∈ N , then am ∈M -rad(N) or bm ∈M -rad(N) or ...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.

The use of synthetic biological systems in research, healthcare, and manufacturing often requires autonomous history-dependent behavior and therefore some form of engineered biological memory. For example, the study or reprogramming of aging, cancer, or development would benefit from genetically encoded counters capable of recording up to several hundred cell division or differentiation events....

Introduction: The current study investigated the combination of high Z atoms (iodine-, platinium-based drugs) with using low energy irradiation (120kvp) in Anaplastic Thyroid cancer cells.Materials and Methods: For this purpose, eight groups were designed: control (CNT), different concentrations of Iodine contrast media (ICM),  irradiation with various doses, Cis-platin (CDDP) with different c...

Extending work of Puninski, Puninskaya and Toffalori in [PPT07], we show that if V is an effectively given valuation domain then the theory of all V -modules is decidable if and only if there exists an algorithm which, given a, b ∈ V , answers whether a ∈ rad(bV ). This was conjectured in [PPT07] for valuation domains with dense value group where it was proved for valuation domains with dense a...