Results 221 to 230 of about 3,987 (248)

Generalization of Artinian rings and the formal power series rings

Rendiconti del Circolo Matematico di Palermo Series 2, 2022
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Maaref, Walid, Hamed, Ahmed, Benhissi, Ali   +2 more
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On Nilpotent Elements, Weak Symmetry and Related Properties of Skew Generalized Power Series Rings

Symmetry
The skew generalized power series ring R[[S,ω]] is a ring construction involving a ring R, a strictly ordered monoid (S,≤), and a monoid homomorphism ω:S→End(R).
Ryszard Mazurek, Mazurek Ryszard
exaly   +2 more sources

Quasi-Armendariz generalized power series rings

Journal of Algebra and Its Applications, 2016
Let [Formula: see text] be a ring, [Formula: see text] a strictly ordered monoid and [Formula: see text] a monoid homomorphism. The skew generalized power series ring [Formula: see text] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal’cev–Neumann Laurent ...
Paykan, K., Moussavi, A.
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Krull property of generalized power series rings

Journal of Pure and Applied Algebra, 2023
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Park, M. H., Oh, D. Y.
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RADICALS OF SKEW GENERALIZED POWER SERIES RINGS

Journal of Algebra and Its Applications, 2012
Let R be a ring, (S, ≤) a strictly ordered monoid and ω : S → End (R) a monoid homomorphism. In this note for a (S, ω)-Armendariz ring R we study some properties of skew generalized power series ring R[[S, ω]]. In particular, among other results, we show that for a S-compatible (S, ω)-Armendariz ring R, α(R[[S, ω]]) = α(R)[[S, ω]] = Ni ℓ*(R)[[S, ω ...
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An Alternative Perspective on Skew Generalized Power Series Rings

Mediterranean Journal of Mathematics, 2016
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Alhevaz, Abdollah, Hashemi, Ebrahim
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On semilocal, Bézout and distributive generalized power series rings

International Journal of Algebra and Computation, 2015
Let R be a ring, and let S be a strictly ordered monoid. The generalized power series ring R[[S]] is a common generalization of polynomial rings, Laurent polynomial rings, power series rings, Laurent series rings, Mal'cev–Neumann series rings, monoid rings and group rings.
Ryszard Mazurek, Michal Ziembowski
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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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Triangular Matrix Representations of Rings of Generalized Power Series

Acta Mathematica Sinica, English Series, 2006
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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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