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排序方式: 共有267条查询结果,搜索用时 46 毫秒
91.
《代数通讯》2013,41(6):2553-2573
The first note shows that the integral closure L′ of certain localities L over a local domain R are unmixed and analytically unramified, even when it is not assumed that R has these properties. The second note considers a separably generated extension domain B of a regular domain A, and a sufficient condition is given for a prime ideal p in A to be unramified with respect to B (that is, p B is an intersection of prime ideals and B/P is separably generated over A/p for all P ∈ Ass (B/p B)). Then, assuming that p satisfies this condition, a sufficient condition is given in order that all but finitely many q ∈ S = {q ∈ Spec(A), p ? q and height(q/p) = 1} are unramified with respect to B, and a form of the converse is also considered. The third note shows that if R′ is the integral closure of a semi-local domain R, then I(R) = ∩{R′ p′ ;p′ ∈ Spec(R′) and altitude(R′/p′) = altitude(R′) ? 1} is a quasi-semi-local Krull domain such that: (a) height(N *) = altitude(R) for each maximal ideal N * in I(R); and, (b) I(R) is an H-domain (that is, altitude(I(R)/p *) = altitude(I(R)) ? 1 for all height one p * ∈ Spec(I(R))). Also, K = ∩{R p ; p ∈ Spec(R) and altitude(R/p) = altitude(R) ? 1} is a quasi-semi-local H-domain such that height (N) = altitude(R) for all maximal ideals N in K. 相似文献
92.
93.
A right R-module satisfies the right Beachy–Blair condition if each of its faithful submodules is cofaithful. In this article we study the relationship between the right Beachy–Blair condition of a right R-module and its skew polynomial, skew monoid and skew generalized power series extensions. Consequently, several known results regarding rings satisfying the right Beachy–Blair condition are extended to a more general setting. 相似文献
94.
Given a significative class ℱ of commutative rings, we study the precise conditions under which a commutative ring R has an ℱ-envelope. A full answer is obtained when ℱ is the class of fields, semisimple commutative rings or integral domains. When ℱ is the class of Noetherian rings, we give a full answer when the Krull dimension of R is zero and when the envelope is required to be epimorphic. The general problem is reduced to identifying the class of non-Noetherian
rings having a monomorphic Noetherian envelope, which we conjecture is the empty class. 相似文献
95.
R. KHOSRAVI 《数学研究及应用》2012,32(4):392-398
In this paper we introduce a class of right S-acts called retractable S-acts which are right S-acts with homomorphisms into their all subacts. We also give some classifications of monoids by comparing such acts with flatness properties. 相似文献
96.
Lex E. Renner 《Journal of Algebraic Combinatorics》2009,29(4):413-435
Let (W,S) be a finite Weyl group and let w∈W. It is widely appreciated that the descent set
determines a very large and important chapter in the study of Coxeter groups. In this paper we generalize some of those results
to the situation of the Bruhat poset W
J
where J⊆S. Our main results here include the identification of a certain subset S
J
⊆W
J
that convincingly plays the role of S⊆W, at least from the point of view of descent sets and related geometry. The point here is to use this resulting descent system (W
J
,S
J
) to explicitly encode some of the geometry and combinatorics that is intrinsic to the poset W
J
. In particular, we arrive at the notion of an augmented poset, and we identify the combinatorially smooth subsets J⊆S that have special geometric significance in terms of a certain corresponding torus embedding X(J). The theory of J-irreducible monoids provides an essential tool in arriving at our main results. 相似文献
97.
Bruno Vallette 《Applied Categorical Structures》2009,17(1):43-61
We give an explicit construction of the free monoid in monoidal abelian categories when the monoidal product does not necessarily
preserve coproducts. Then we apply it to several new monoidal categories that appeared recently in the theory of Koszul duality
for operads and props. This gives a conceptual explanation of the form of the free operad, free dioperad and free properad.
相似文献
98.
Let B be a domain, Q a maximal ideal of B, π: B → B/Q the canonical surjection, D a subring of B/Q, and A:=π
−1(D). If both B and D are almost-divided domains (resp., n-divided domains), then A = B ×
B/Q
D is an almost-divided domain (resp., an n-divided domain); the converse holds if B is quasilocal. If 2 ≤ d ≤ ∞, an example is given of an almost-divided domain of Krull dimension d which is not a divided domain.
相似文献
99.
100.
《Journal of Pure and Applied Algebra》2022,226(4):106887
In the present work, we prove that every class of the divisor class group of a Krull monoid algebra contains infinitely many prime divisors. Several attempts to this result have been made in the literature so far, unfortunately with open gaps. We present a complete proof of this fact. 相似文献