共查询到20条相似文献,搜索用时 15 毫秒
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Takanori Nagamine 《代数通讯》2018,46(10):4265-4272
In this paper, we study some properties of coordinates in the polynomial ring by introducing some concepts which are weaker than coordinates. In particular, in the polynomial ring in two variables over an algebraically closed field of characteristic zero, we show some relations between polynomials and their fibers on 𝔸2. 相似文献
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Huanyin Chen 《Czechoslovak Mathematical Journal》2008,58(4):899-910
Let R be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in R is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related
comparability. 相似文献
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N. S. Gopala Krishnan 《Proceedings Mathematical Sciences》1962,56(3):148-154
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A. N. Abyzov 《Siberian Mathematical Journal》2012,53(5):763-771
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The paper characterizes the length of maximal sequences satisfying conditions (i) and (ii) of (FC)-sequences, and proves some properties of (FC)-sequences, such as a bound on their lengths. As a consequence we get some results for mixed multiplicities and multiplicities of Rees rings of equimultiple ideals. We also prove that if is an ideal of positive height and is an arbitrary maximal sequence in satisfying conditions (i) and (ii) of (FC)-sequences, then is a reduction of
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Algebra universalis - 相似文献
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The main purpose of this paper is to prove the following result. Let R be a prime ring of characteristic different from two and let T : R → R be an additive mapping satisfying the relation T(x
3) = T(x)x
2 − xT(x)x + x
2
T(x) for all x ∈ R. In this case T is of the form 4T(x) = qx + xq, where q is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional
equations in prime rings with involution which are related to bicircular projections. 相似文献
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Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan 《Journal of Pure and Applied Algebra》2018,222(4):889-899
Let v be a Krull valuation of a field with valuation ring . Let θ be a root of an irreducible trinomial belonging to . In this paper, we give necessary and sufficient conditions involving only for to be integrally closed. In the particular case when v is the p-adic valuation of the field of rational numbers, and , then it is shown that these conditions lead to the characterization of primes which divide the index of the subgroup in , where is the ring of algebraic integers of K. As an application, it is deduced that for any algebraic number field K and any quadratic field L not contained in K, we have if and only if the discriminants of K and L are coprime. 相似文献
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For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results by giving the whole graded minimal free resolutions explicitly. Then we use these resolutions to determine some invariants of the semigroups and certain interesting relations among them. Finally, we determine semigroups of small embedding dimensions which have strongly indispensable resolutions. 相似文献
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John C. McConnell 《Mathematische Zeitschrift》1977,153(3):253-254
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Ernst Kleinert 《Archiv der Mathematik》1987,49(3):200-207
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L.J. Ratliff Jr 《代数通讯》2013,41(18):1977-2005
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It is known that for a simple module S over a commutative ring R, fd R (S) = id R (S). Let R T be commutative rings and R→T a ring homomorphism, if T is a Noetherian ring and self-injective, then fd R (T) = id R (T). In this paper we use the equalities of mixed functors to generalise these results over non-commutative rings 相似文献
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Gennady Lyubeznik 《Mathematische Zeitschrift》2006,254(3):627-640
Let A be a commutative Noetherian local ring containing a field of characteristic p>0. The integer invariants λ
i,j
(A) have been introduced in an old paper of ours. In this paper we completely describe λ
d,d
(A) where d=dimA in terms of the topology of SpecA.
NSF support through grant DMS-0202176 is gratefully acknowledged 相似文献