The aim of this paper is to investigate strong notion strongly ⨁-supplemented modules in module theory, namely ⨁-locally artinian supplemented modules. We call a M if it locally and its supplement submodules are direct summand. In study, we provide the basic properties particular, show that every summand supplemented. Moreover, prove ring R semiperfect with radical only projective R-module

Let M be a right module over a ring R. In this manuscript, we shall study on a special case of F-inverse split modules where F is a fully invariant submodule of M introduced in [12]. We say M is Z 2(M)-inverse split provided f^(-1)(Z2(M)) is a direct summand of M for each endomorphism f of M. We prove that M is Z2(M)-inverse split if and only if M is a direct...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular.It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.

Given a k-graph Λ and an element p of N, we define the dual k-graph, pΛ. We show that when Λ is row-finite and has no sources, the C∗-algebras C∗(Λ) and C∗(pΛ) coincide. We use this isomorphism to apply Robertson and Steger’s results to calculate the K-theory of C∗(Λ) when Λ is finite and strongly connected and satisfies the aperiodicity condition.

Let Y denote a D-class symmetric association scheme with D ≥ 3, and suppose Y is almostbipartite Pand Q-polynomial. Let x denote a vertex of Y and let T = T (x) denote the corresponding Terwilliger algebra. We prove that any irreducible T -module W is both thin and dual thin in the sense of Terwilliger. We produce two bases for W and describe the action of T on these bases. We prove that the is...

Let R be a commutative ring. For two (left) R-modules M and N , the set HomR(M,N) of allR-linear maps fromM toN is anR-module under natural addition and scaling operations on linear maps. (If R were non-commutative then the definition (r · f)(m) = r · (f(m)) would yield a function r · f from M to N which is usually not R-linear. Try it!) In the special case where N = R we get the R-module M∨ = ...

Many observations about coalgebras were inspired by comparable situations for algebras. Despite the prominent role of prime algebras, the theory of a corresponding notion for coalgebras was not well understood so far. Coalgebras C over fields may be called coprime provided the dual algebra C∗ is prime. This definition, however, is not intrinsic it strongly depends on the base ring being a field...

In this paper we focus on a special class of commutative local‎ ‎rings called SPAP-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎We characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an SPAP-ring and derive some basic properties‎. ‎Then we answer the‎ ‎question of Lam and Reyes about strongly Oka ideals fam...