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Skew inverse power series rings over a ring with projective socle

Kamal Paykan (2017)

Czechoslovak Mathematical Journal

A ring $R$ is called a right $PS$ -ring if its socle, $Soc (R_{R})$ , is projective. Nicholson and Watters have shown that if $R$ is a right $PS$ -ring, then so are the polynomial ring $R [x]$ and power series ring $R [[x]]$ . In this paper, it is proved that, under suitable conditions, if $R$ has a (flat) projective socle, then so does the skew inverse power series ring $R [[x^{- 1}; α, δ]]$ and the skew polynomial ring $R [x; α, δ]$ , where $R$ is an associative ring equipped with an automorphism $α$ and an $α$ -derivation $δ$ . Our results extend and unify many existing results....

Slender modules, endo-slender abelian groups and large cardinals

Katsuya Eda (1990)

Fundamenta Mathematicae

Small almost free modules with prescribed topological endomorphism rings

A. L. S. Corner, Rüdiger Göbel (2003)

Rendiconti del Seminario Matematico della Università di Padova

Smash products for $G$ -sets, Clifford theory and duality theorems.

Năstăsescu, C., Van Oystaeyen, Fred, Zhou, Borong (1995)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Smash products, group actions and group graded rings.

Soren Jondrup, Anders Jensen (1991)

Mathematica Scandinavica

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.

Some algebraic applications of graded categorical group theory.

Cegarra, A.M., Garzón, A.R. (2003)

Theory and Applications of Categories [electronic only]

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...