Results 221 to 230 of about 9,861,726 (254)

Triangular Matrix Representations of Rings of Generalized Power Series

Acta Mathematica Sinica, English Series, 2006
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Zhong Kui Liu
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Special Properties of Rings of Generalized Power Series

Communications in Algebra, 2004
Abstract Let R be a ring and (S, ≤) a strictly ordered monoid. Properties of the ring [[R S,≤]] of generalized power series with coefficients in R and exponents in S are considered in this paper. It is shown that [[R S,≤]] is reduced (2-primal, Dedekind finite, clean, uniquely clean) if and only if R is reduced (2-primal, Dedekind finite, clean ...
Zhongkui Liu
exaly   +2 more sources

Noetherian Generalized Power Series Rings

Communications in Algebra, 2004
Abstract Let R be a unitary ring and (M, ≤) a strictly ordered monoid. We show that, if (M, ≤) is positively ordered, then the generalized power series ring R[[M, ≤]] is left Noetherian, if and only if, R is left Noetherian and M is finitely generated, if and only if, R is left Noetherian and R[[M, ≤]] is a homomorphic image of the power series ring R[[
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On root closedness in generalized power series rings

Communications in Algebra
Mi Hee Park
exaly   +3 more sources

Krull Domains of Generalized Power Series [PDF]

Journal of Algebra, 2001
For an integral domain D and a torsion-free cancellative strictly subtotally ordered monoid (S,≤), it is shown that the generalized power series ring [[DS,≤]] is a Krull domain if and only if D is a Krull domain and S is a Krull ...
Hwankoo Kim
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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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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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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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