Rings with unique addition
نویسندگان
چکیده
منابع مشابه
On Involution Rings with Unique Minimal *-subring
The structure of certain involution rings having a unique minimal *-subring, is described.
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Let K be a field of characteristic zero and let K((R≤0)) denote the ring of generalized power series (i.e., formal sums with well-ordered support) with coefficients in K, and non-positive real exponents. Berarducci (2000) constructed an irreducible omnific integer, in the sense of Conway (2001), by first proving that an element of K((R≤0)) that is not divisible by a monomial and whose support h...
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In this note we prove that every regular local ring of dimension 3 is a unique factorization domain. Nagata4 showed (Proposition 11) that if every regular local ring of dimension 3 is a unique factorization domain, then every regular local ring has unique factorization.* Thus, combining these results we have that every regular local ring is a unique factorization domain. Throughout this note R ...
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Let G be a finite group, k a perfect field, and V a finite dimensional kG-module. We let G act on the power series k[[V ]] by linear substitutions and address the question of when the invariant power series k[[V ]] form a unique factorization domain. We prove that for a permutation module for a p-group in characteristic p, the answer is always positive. On the other hand, if G is a cyclic group...
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Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors. The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero zero-divisors of $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$. In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1958
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1958-0095868-0