The valuated ring of the arithmetical functions as a power series ring

Emil Daniel Schwab; Gheorghe Silberberg

Displaying similar documents to “The valuated ring of the arithmetical functions as a power series ring”

When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

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A lattice-ordered ring $ℝ$ is called an if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those $f$ -rings $ℝ$ such that $ℝ / 𝕀$ is contained in an $f$ -ring with an identity element that is a strong order unit for some nil $l$ -ideal $𝕀$ of $ℝ$ . In particular, if $P (ℝ)$ denotes the set of nilpotent elements of the $f$ -ring $ℝ$ , then $ℝ$ is an OIRI-ring if and only if $ℝ / P (ℝ)$ is contained in an $f$ -ring with an identity element that is a strong order unit. ...

A note on semilocal group rings

Angelina Y. M. Chin (2002)

Czechoslovak Mathematical Journal

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Let $R$ be an associative ring with identity and let $J (R)$ denote the Jacobson radical of $R$ . $R$ is said to be semilocal if $R / J (R)$ is Artinian. In this paper we give necessary and sufficient conditions for the group ring $R G$ , where $G$ is an abelian group, to be semilocal.

On a theorem of McCoy

Rajendra K. Sharma, Amit B. Singh (2024)

Mathematica Bohemica

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We study McCoy’s theorem to the skew Hurwitz series ring $(HR, ω)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring $R$ satisfies McCoy’s theorem of skew Hurwitz series.

σ-ring and σ-algebra of Sets1

Noboru Endou, Kazuhisa Nakasho, Yasunari Shidama (2015)

Formalized Mathematics

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In this article, semiring and semialgebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semiring of sets has already been formalized in [13], that is, strictly speaking, a definition of a quasi semiring of sets suggested in the last few decades [15]. We adopt a classical definition of a semiring of sets here to avoid such a confusion. Ring of sets and algebra of sets have been formalized as non empty preboolean set [23] and field of subsets...