Displaying 21 – 40 of 1154

Showing per page

A general form of non-Frobenius self-injective algebras

Andrzej Skowroński, Kunio Yamagata (2006)

Colloquium Mathematicae

Applying the classical work of Nakayama [Ann. of Math. 40 (1939)], we exhibit a general form of non-Frobenius self-injective finite-dimensional algebras over a field.

A generalization of Mathieu subspaces to modules of associative algebras

Wenhua Zhao (2010)

Open Mathematics

We first propose a generalization of the notion of Mathieu subspaces of associative algebras 𝒜 , which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to 𝒜 -modules . The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets σ(N) and τ(N) of stable...

A graph associated to proper non-small ideals of a commutative ring

S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel (2017)

Commentationes Mathematicae Universitatis Carolinae

In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring R , denoted by G ( R ) , is a graph with all non-small proper ideals of R as vertices and two distinct vertices I and J are adjacent if and only if I J is not small in R . In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of rings are studied. We investigated the basic properties of the small intersection graph as diameter,...

A Morita equivalence for Hilbert C*-modules

Maria Joiţa, Mohammad Sal Moslehian (2012)

Studia Mathematica

We introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate the properties of the new Morita equivalence. We apply our results to study continuous actions of locally compact groups on full Hilbert C*-modules. We also present an extension of Green's theorem in the context of Hilbert C*-modules.

A Morita type theorem for a sort of quotient categories

Simion Breaz (2005)

Czechoslovak Mathematical Journal

We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.

Currently displaying 21 – 40 of 1154