In this paper, we assume that algebras are finite dimensional algebras with 1 over a fixed field k and modules over an algebra are finitely generated left unitary modules. Let A and B be two algebras (where k is a splitting field for A and B) with no semisimple summands. If two bimodules AMB and BNA induce a stable equivalence of Morita type between A and B, and if N⊗A− maps any simple A-module...

In this paper we define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idemp...

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.  

Abstract. The construction of Freudenthal’s Magic Square, which contains the exceptional simple Lie algebras of types F4, E6, E7 and E8, in terms of symmetric composition algebras is further developed here. The para-Hurwitz algebras, which form a subclass of the symmetric composition algebras, will be defined, in the split case, in terms of the natural two dimensional module for the simple Lie ...

Let Λ be a finite-dimensional (D, A)-stacked monomial algebra. In this paper, we give necessary and sufficient conditions for the variety of a simple Λ-module to be nontrivial. This is then used to give structural information on the algebra Λ, as it is shown that if the variety of every simple module is nontrivial, then Λ is a D-Koszul monomial algebra. We also provide examples of (D, A)-stacke...

The ground field k is algebraically closed and of characteristic zero. Let g be a simple Lie algebra over k. The goal of this note is to prove a closed formula for the Dynkin index of a principal sl2-subalgebra of g, see Theorem 3.2. The key step in the proof uses the “strange formula” of Freudenthal–de Vries. As an application, we (1) compute the Dynkin index any simple g-module regarded as sl...

Abstract We formulate an interpretation of the theory of physical superselection sectors in terms of vertex operator algebra language. Using this formulation we give a construction of simple current from a primary semisimple element of weight one. We then prove that if a rational vertex operator algebra V has a simple current M satisfying certain conditions, then V ⊕M has a natural rational ver...

We study certain ltrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warreld. To indicate the consequences of our analysis, suppose that g is a complex classical simple Lie superalgebra and that E is an indecomposable injective g-module with nonzero (and so necessarily simp...

We study certain filtrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warfield. To indicate the consequences of our analysis, suppose that g is a complex classical simple Lie superalgebra and that E is an indecomposable injective g-module with nonzero (and so necessarily s...