共查询到20条相似文献,搜索用时 46 毫秒
1.
Over a commutative ring R, a module is artinian if and only if it is a Loewy module with finite Loewy invariants [5]. In this paper, we show that this is not necesarily true for modules over noncommutative rings R, though every artinian module is always a Loewy module with finite Loewy invariants. We prove that every Loewy module with finite Loewy invariants has a semilocal endomorphism ring, thus generalizing a result proved by Camps and Dicks for artinian modules [3]. Finally, we obtain similar results for the dual class of max modules. 相似文献
2.
In this article, we give a criterion that characterizes equivalent weak crossed products. By duality, we obtain a similar result for weak crossed coproducts and, as a consequence, we find the conditions that assures the equivalence between two weak crossed biproducts. As an application, we show that the main results proved by Panaite in [12] (see also [11]), for Brzeziński's crossed products, admits a substantial reduction in the imposed conditions. 相似文献
3.
A ring R with identity is called “clean” if every element of R is the sum of an idempotent and a unit, and R is called “strongly clean” if every element of R is the sum of an idempotent and a unit that commute. Strongly clean rings are “additive analogs” of strongly regular rings, where a ring R is strongly regular if every element of R is the product of an idempotent and a unit that commute. Strongly clean rings were introduced in Nicholson (1999) where their connection with strongly π-regular rings and hence to Fitting's Lemma were discussed. Local rings and strongly π-regular rings are all strongly clean. In this article, we identify new families of strongly clean rings through matrix rings and triangular matrix rings. For instance, it is proven that the 2 × 2 matrix ring over the ring of p-adic integers and the triangular matrix ring over a commutative semiperfect ring are all strongly clean. 相似文献
4.
We consider the Shigesada-Kawasaki-Teramoto cross-diffusion model for two competing species. If both species have the same random diffusion coefficients and the space dimension is less than or equal to three, we establish the global existence and uniform boundedness of smooth solutions to the model in convex domains. This extends some previous works of Kim [12] and Shim [21] in one dimensional space. 相似文献
5.
Zenghui Gao 《代数通讯》2013,41(8):3035-3044
This article continues to investigate a particular case of Gorenstein FP-injective modules, called strongly Gorenstein FP-injective modules. Some examples are given to show that strongly Gorenstein FP-injective modules lie strictly between FP-injective modules and Gorenstein FP-injective modules. Various results are developed, many extending known results in [1]. We also characterize FC rings in terms of strongly Gorenstein FP-injective, projective, and flat modules. 相似文献
6.
Michał Ziembowski 《代数通讯》2013,41(2):664-666
One of the main results of the article [2] says that, if a ring R is semiperfect and ? is an authomorphism of R, then the skew Laurent series ring R((x, ?)) is semiperfect. We will show that the above statement is not true. More precisely, we will show that, if the Laurent series ring R((x)) is semilocal, then R is semiperfect with nil Jacobson radical. 相似文献
7.
8.
Dimitrios Ballas 《代数通讯》2013,41(8):2815-2824
The notion of cohomological periodicity after 1-step has been studied by Talelli in [7, 8], and [9]. If a group G has periodic cohomology after 1-step, then G is the fundamental group of a graph of finite groups, which have periodic cohomology of the same period. Also, the fundamental group of a tree of finite groups, which have periodic cohomology of the same period, has periodic cohomology after 1-step. In this paper, we show that if a group G has only cyclic finite subgroups and is the fundamental group of a certain tree of groups, which have -steps. 相似文献
9.
Anders O. F. Hendrickson 《代数通讯》2013,41(12):4420-4438
Diaconis and Isaacs have defined the supercharacter theories of a finite group to be certain approximations to the ordinary character theory of the group [7]. We make explicit the connection between supercharacter theories and Schur rings, and we provide supercharacter theory constructions which correspond to Schur ring products of Leung and Man [12], Hirasaka and Muzychuk [10], and Tamaschke [20]. 相似文献
10.
Let R be a ring, S a strictly ordered monoid, and ω: S → End(R) a monoid homomorphism. In [30], Marks, Mazurek, and Ziembowski study the (S, ω)-Armendariz condition on R, a generalization of the standard Armendariz condition from polynomials to skew generalized power series. Following [30], we provide various classes of nonreduced (S, ω)-Armendariz rings, and determine radicals of the skew generalized power series ring R[[S ≤, ω]], in terms of those of an (S, ω)-Armendariz ring R. We also obtain some characterizations for a skew generalized power series ring to be local, semilocal, clean, exchange, uniquely clean, 2-primal, or symmetric. 相似文献
11.
Weixing Chen 《代数通讯》2013,41(7):2347-2350
A new characterization of a strongly clean ring is given. And it is proven that if R is a strongly clean ring, then eRe is a strongly clean ring for e 2 = e ∈ R, which answers a question of Nicholson (1999) in the affirmative. 相似文献
12.
Jean-Yves Chemin 《偏微分方程通讯》2015,40(5):878-896
By applying Wiegner's method in [16], we first prove the large time decay estimate for the global solutions of a 2.5 dimensional Navier-Stokes system, which is a sort of singular perturbed 2-D Navier-Stokes system in three space dimension. As an application of this decay estimate, we give a simplified proof for the global wellposedness result in [6] for 3-D Navier-Stokes system with one slow variable. Let us also mention that compared with the assumptions for the initial data in [6], here the assumptions in Theorem 1.3 are weaker. 相似文献
13.
Vyacheslav Futorny 《代数通讯》2013,41(8):3381-3385
In this note we extend the results of Bekkert and Futorny in [2] and Hemmer, Kujawa and Nakano in [10] and determine the derived representation type of Schur superalgebras. 相似文献
14.
FRANK TUTZAUER 《The Journal of mathematical sociology》2013,37(3):249-266
Axelrod's (1980a 1980b) Prisoner's Dilemma computer tournaments have motivated numerous investigations of cooperation, strategy choice, and strategic evolution. By having players adopt various strategies for playing the Prisoner's Dilemma, and then programming a computer to pit the strategies against each other in a round-robin format, Axelrod uncovered important principles about the evolution of cooperation in certain contexts, and stimulated others to extend his basic method into other settings. This article presents a matrix approach for calculating the results of an Axelrod-type tournament. This approach allows one to investigate the impact of changes in the format of the tournament, the nature of the payoff matrix, or the particular strategic choices of the players. 相似文献
15.
Jiaqun Wei 《代数通讯》2013,41(7):2456-2465
Let R be an exchange ring. In this article, we show that the following conditions are equivalent: (1) R has stable range not more than n; (2) whenever x ∈ R n is regular, there exists some unimodular regular w ∈ n R such that x = xwx; (3) whenever x ∈ R n is regular, there exist some idempotent e ∈ R and some unimodular regular w ∈ R n such that x = ew; (4) whenever x ∈ R n is regular, there exist some idempotent e ∈ M n (R) and some unimodular regular w ∈ R n such that x = we; (5) whenever a( n R) + bR = dR with a ∈ R n and b,d ∈ R, there exist some z ∈ R n and some unimodular regular w ∈ R n such that a + bz = dw; (6) whenever x = xyx with x ∈ R n and y ∈ n R, there exist some u ∈ R n and v ∈ n R such that vxyu = yx and uv = 1. These, by replacing unimodularity with unimodular regularity, generalize the corresponding results of Canfell (1995, Theorem 2.9), Chen (Chen 2000, Theorem 4.2 and Proposition 4.6, Chen 2001, Theorem 10), and Wu and Xu (1997, Theorem 9), etc. 相似文献
16.
Yuly Billig 《代数通讯》2018,46(8):3413-3429
We reprove the results of Jordan [18] and Siebert [30] and show that the Lie algebra of polynomial vector fields on an irreducible a?ne variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not depend on papers mentioned above. Besides, the structure of the module of polynomial functions on an irreducible smooth a?ne variety over the Lie algebra of vector fields is studied. Examples of Lie algebras of polynomial vector fields on an N-dimensional sphere, non-singular hyperelliptic curves and linear algebraic groups are considered. 相似文献
17.
Martin G. Everett Philip Sinclair Peter Dankelmann 《The Journal of mathematical sociology》2013,37(4):215-227
We prove a number of results on betweenness and closeness centrality and centralization. In particular, we prove the much used normalization expression for closeness centrality first given by Freeman (1979), correcting an error in the justification given in his paper. We explore the relationship between betweenness and the cutting number and use these results to prove and correct some centrality and centralization formulae first proposed by Borgatti and Everett (1997). 相似文献
18.
The article considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control problems. By a counter example of Serrin [18], it is known that, in the presence of non-smooth data, a standard weak formulation does not ensure uniqueness for such equations. Therefore several notions of solution have been developed that guarantee uniqueness. In this note, we compare different definitions of solutions, namely the ones of Stampacchia [19] and Boccardo-Galouët [4] and the two notions of solutions of [2, 7], and show that they are equivalent. As side results, we reformulate the solution in the sense of [19], and prove the existence of solutions in the sense of [2, 4, 7] in case of mixed boundary conditions. 相似文献
19.
Mamoru Furuya 《代数通讯》2013,41(8):3130-3146
Let A be an analytic algebra over a field k of characteristic p > 0. In this article, for an analytic k-algebra we introduce the concept of analytic pn-basis which generalizes the pn-basis defined in [1], and the concept of an pn-admissible field for an algebraic function field, we give regularity criteria and absolute regularity criteria for an analytic algebra A/k in terms of the higher differential algebra and analytic pn-basis. The results are partial extension of our previous results for affine algebras to the case of analytic algebras (cf. [1, 3]), and these are partial generalization of results of Orbanz in the analytic case (cf. [9]). 相似文献
20.
A ring is called clean if every element is a sum of a unit and an idempotent, while a ring is said to be weakly clean if every element is either a sum or a difference of a unit and an idempotent. Commutative weakly clean rings were first discussed by Anderson and Camillo [2] and were extensively investigated by Ahn and Anderson [1], motivated by the work on clean rings. In this paper, weakly clean rings are further discussed with an emphasis on their relations with clean rings. This work shows new interesting connections between weakly clean rings and clean rings. 相似文献