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Displaying 2721 – 2740 of 3997

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Slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały, Karolina Szmyt (2007)

Open Mathematics

We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module.

Smooth invariants and ω -graded modules over k [ X ]

Fred Richman (2000)

Commentationes Mathematicae Universitatis Carolinae

It is shown that every ω -graded module over k [ X ] is a direct sum of cyclics. The invariants for such modules are exactly the smooth invariants of valuated abelian p -groups.

Solutions of minus partial ordering equations over von Neumann regular rings

Yu Guan, Zhaojia Tong (2015)

Open Mathematics

In this paper, we mainly derive the general solutions of two systems of minus partial ordering equations over von Neumann regular rings. Meanwhile, some special cases are correspondingly presented. As applications, we give some necessary and sufficient conditions for the existence of solutions. It can be seen that some known results can be regarded as the special cases of this paper.

Some characterizations of regular modules.

Goro Azumaya (1990)

Publicacions Matemàtiques

Let M be a left module over a ring R. M is called a Zelmanowitz-regular module if for each x ∈ M there exists a homomorphism F: M → R such that f(x) = x. Let Q be a left R-module and h: Q → M a homomorphism. We call h locally split if for every x ∈ M there exists a homomorphism g: M → Q such that h(g(x)) = x. M is called locally projective if every epimorphism onto M is locally split. We prove that the following conditions are equivalent:(1) M is Zelmanowitz-regular.(2) every homomorphism into M...

Currently displaying 2721 – 2740 of 3997