Results 1 to 10 of about 9,258 (222)

Generalized Power Series Rings

1990
Let R be a commutative ring, with unit element 1. Let S be a commutative monoid written multiplicatively (except when written additively...); thus, S is a semigroup with unit element, also denoted 1. We assume that S is endowed with a compatible strict order relation ≤, which is not necessarily a total order.
openaire   +1 more source

On app skew generalized power series rings

Studia Scientiarum Mathematicarum Hungarica, 2013
By [12], a ring R is left APP if R has the property that “the left annihilator of a principal ideal is pure as a left ideal”. Equivalently, R is a left APP-ring if R modulo the left annihilator of any principal left ideal is flat. Let R be a ring, (S, ≦) a strictly totally ordered commutative monoid and ω: S → End(R) a monoid homomorphism.
A. Majidinya, A. Moussavi
openaire   +1 more source

Rings of generalized power series: Nilpotent elements

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1991
The author studies the set \(A\) of generalized power series, with coefficients in a commutative ring and exponents in an ordered commutative monoid. \(A\) is a commutative ring with pointwise addition and natural convolution. Particular cases are polynomial rings over semigroups, formal power series on finite or infinite variables.
openaire   +2 more sources

NOETHERIAN GENERALIZED POWER SERIES RINGS AND MODULES

Communications in Algebra, 2001
In this paper we considerably strengthen a result of Ribenboim on noetherian generalised power series rings. While Ribenboim proves his result under the restrictive assumption that the monoid occuring in the definition of the geralised power series ring in cancellative we prove a corresponding result for arbitrary ordered monoids.
openaire   +1 more source

Rota–Baxter operators on skew generalized power series rings

Journal of Algebra and Its Applications, 2014
Let R be a ring, S a strictly ordered monoid, and ω : S → End (R) a monoid homomorphism. The skew generalized power series ring R[[S, ω]] is a common generalization of (skew) polynomial rings, (skew) Laurent polynomial rings, (skew) power series rings, (skew) Laurent series rings, (skew) monoid rings, (skew) Mal'cev–Neumann series rings, and ...
openaire   +2 more sources

TRIANGULAR MATRIX REPRESENTATION OF SKEW GENERALIZED POWER SERIES RINGS

Asian-European Journal of Mathematics, 2012
Let R be a ring, (S, ≤) a strictly ordered monoid and ω : S → End (R) a monoid homomorphism. In this paper, we study the triangular matrix representation of skew generalized power series ring R[[S, ω]] which is a compact generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomials rings, (skew) Laurent power series ...
openaire   +2 more sources

Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings

Advances in Pure Mathematics, 2022
Eltiyeb Ali
exaly  

Ps-rings of generalized power series

Communications in Algebra, 1998
Lin Zhongkui, Li Fang
openaire   +1 more source

Root extension of generalized power series rings

Communications in Algebra, 2023
openaire   +1 more source

EXTENSIONS OF GM-RINGS OVER GENERALIZED POWER SERIES RINGS

2007
Let R be a reduced ring, (S, ≤) a cancellative torsion-free strictly ordered monoid, it is shown that ring [[RS,≤]] is a GM− ring if and only if R is a GM−ring. We also investigate GM− rings for some special Morita Contexts and module extensions over generalized power series rings.
Ouyang, Lunqun, Liu, Dayong
openaire   +1 more source