Weak dimension and right distributivity of skew generalized power series rings
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- Mazurek Ryszard
- Faculty of Computer Science, Białystok University of Technology
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- Ziembowski Michał
- Maxwell Institute of Sciences, School of Mathematics, University of Edinburgh
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Abstract
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 power series rings, skew Laurent polynomial rings, skew group rings, and Mal'cev-Neumann Laurent series rings. In the case where S is positively ordered we give sufficient and necessary conditions for the skew generalized power series ring R[[S, ω]] to have weak dimension less than or equal to one. In particular, for such an S we show that the ring R[[S, ω]] is right duo of weak dimension at most one precisely when the lattice of right ideals of the ring R[[S, ω]] is distributive and ω(s) is injective for every s ∈ S.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 62 (4), 1093-1112, 2010
The Mathematical Society of Japan
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Details 詳細情報について
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- CRID
- 1390001205116109696
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- NII Article ID
- 10027871025
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL BIB ID
- 10859015
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed