Results 231 to 240 of about 9,360 (253)

Morita Duality for the Rings of Generalized Power Series

Acta Mathematica Sinica, English Series, 2002
Let \(A,B\) be associative rings with identity, and \((S,\leq)\) be a strictly totally ordered monoid which is also Artinian and finitely generated. Then one forms a ring, denoted by \([[A^{S,\leq}]]\), called the ring of generalized power series. For any bimodule \(_AM_B\), one forms a bimodule \(_{[[A^{S,\leq}]]}[M^{S,\leq}]_{[[B^{S,\leq}]]}\).
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Ordered Rings of Generalized Power Series

1993
In this paper, we consider orders on rings of generalized power series. Unless the contrary is expressly stated, we do not assume the orders to be total (=linear); for brevity we omit the qualification “partial” order. The first section deals with the order introduced by Conrad, Harvey & Holland on abelian additive groups of maps from an ordered set (S,
A. Benhissi, P. Ribenboim
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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.
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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
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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.
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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.
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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 ...
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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 ...
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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
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