Matches in SemOpenAlex for { <https://semopenalex.org/work/W2476371214> ?p ?o ?g. }
- W2476371214 abstract "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 series rings. In this paper, we introduce and study the [Formula: see text]-nil-Armendariz condition on [Formula: see text], a generalization of the standard nil-Armendariz condition from polynomials to skew generalized power series. We resolve the structure of [Formula: see text]-nil-Armendariz rings and obtain various necessary or sufficient conditions for a ring to be [Formula: see text]-nil-Armendariz. The [Formula: see text]-nil-Armendariz condition is connected to the question of whether or not a skew generalized power series ring [Formula: see text] over a nil ring [Formula: see text] is nil, which is related to a question of Amitsur [Algebras over infinite fields, Proc. Amer. Math. Soc. 7 (1956) 35–48]. As particular cases of our general results we obtain several new theorems on the nil-Armendariz condition. Our results extend and unify many existing results." @default.
- W2476371214 created "2016-08-23" @default.
- W2476371214 creator A5061078808 @default.
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- W2476371214 date "2016-08-02" @default.
- W2476371214 modified "2023-09-27" @default.
- W2476371214 title "Nilpotent elements and nil-Armendariz property of skew generalized power series rings" @default.
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- W2476371214 doi "https://doi.org/10.1142/s1793557117500346" @default.
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