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On weakened ( α , δ ) -skew Armendariz rings

Alireza Majdabadi Farahani, Mohammad Maghasedi, Farideh Heydari, Hamidagha Tavallaee (2022)

Mathematica Bohemica

In this note, for a ring endomorphism α and an α -derivation δ of a ring R , the notion of weakened ( α , δ ) -skew Armendariz rings is introduced as a generalization of α -rigid rings and weak Armendariz rings. It is proved that R is a weakened ( α , δ ) -skew Armendariz ring if and only if T n ( R ) is weakened ( α ¯ , δ ¯ ) -skew Armendariz if and only if R [ x ] / ( x n ) is weakened ( α ¯ , δ ¯ ) -skew Armendariz ring for any positive integer n .

On μ -singular and μ -extending modules

Yahya Talebi, Ali Reza Moniri Hamzekolaee (2012)

Archivum Mathematicum

Let M be a module and μ be a class of modules in Mod - R which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a μ -essential submodule provided it has a non-zero intersection with any non-zero submodule in μ . We define and investigate μ -singular modules. We also introduce μ -extending and weakly μ -extending modules and mainly study weakly μ -extending modules. We give some characterizations of μ -co-H-rings by weakly μ -extending modules. Let R ...

One-dimensional infinitesimal-birational duality through differential operators

Tomasz Maszczyk (2006)

Fundamenta Mathematicae

The structure of filtered algebras of Grothendieck's differential operators on a smooth fat point in a curve and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality realized by a Springer type resolution of singularities and the Fourier transformation is presented. This algebro-geometrical duality is quantized in appropriate sense and its quantum origin is explained.

Ordinary selfdistributive rings

Sobhy Ghoneim, Marian Kechlibar, Tomáš Kepka (2005)

Commentationes Mathematicae Universitatis Carolinae

Left selfdistributive rings (i.e., x y z = x y x z ) which are semidirect sums of boolean rings and rings nilpotent of index at most 3 are studied.

Phantom maps and purity in modular representation theory, I

D. Benson, G. Gnacadja (1999)

Fundamenta Mathematicae

Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms we need...

P-injective group rings

Liang Shen (2020)

Czechoslovak Mathematical Journal

A ring R is called right P-injective if every homomorphism from a principal right ideal of R to R R can be extended to a homomorphism from R R to R R . Let R be a ring and G a group. Based on a result of Nicholson and Yousif, we prove that the group ring RG is right P-injective if and only if (a) R is right P-injective; (b) G is locally finite; and (c) for any finite subgroup H of G and any principal right ideal I of RH , if f ∈ Hom R ( I R , R R ) , then there exists g ∈ Hom R ( RH R , R R ) such that g | I = f . Similarly, we also obtain equivalent characterizations...

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