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11.
Houmem Belkhechine 《Discrete Mathematics》2017,340(12):2986-2994
Given a tournament , a module of is a subset of such that for and , if and only if . The trivial modules of are ,
and . The tournament is indecomposable if all its modules are trivial; otherwise it is decomposable. The decomposability index of , denoted by , is the smallest number of arcs of that must be reversed to make indecomposable. For , let be the maximum of over the tournaments with vertices. We prove that and that the lower bound is reached by the transitive tournaments. 相似文献
12.
Derya Keskı̇n Tütüncü 《代数通讯》2017,45(2):688-693
In this paper we provide conditions under which automorphism-coinvariant modules over a right perfect ring are quasi-projective. 相似文献
13.
Chen Huanyin 《东北数学》1997,(2)
PolynomialRingsoverNon┐noetherianPowerSeriesRingsChenHuanyin(陈焕艮)(DepartmentofMathematics,HunanNormalUniversity,Changsha,4100... 相似文献
14.
Let A be an n × d matrix having full rank n. An orthogonal dual A⊥ of A is a (d-n) × d matrix of rank (d−n) such that every row of A⊥ is orthogonal (under the usual dot product) to every row of A. We define the orthogonal dual for arrangements by identifying an essential (central) arrangement of d hyperplanes in n-dimensional space with the n × d matrix of coefficients of the homogeneous linear forms for which the hyperplanes are kernels. When n ≥ 5, we show that if the matroid (or the lattice of intersection) of an n-dimensional essential arrangement contains a modular copoint whose complement spans, then the derivation module of the orthogonally dual arrangement
⊥ has projective dimension at least ⌈ n(n+2)/4 ⌉ - 3.Hal Schenck partially supported by NSF DMS 03-11142, NSA MDA 904-03-1-0006, and ATP 010366-0103. 相似文献
15.
Paul Ramsden 《Journal of Functional Analysis》2010,258(12):3988-4009
Let S be a semigroup. In this paper we investigate the injectivity of ?1(S) as a Banach right module over ?1(S). For weakly cancellative S this is the same as studying the flatness of the predual left module c0(S). For such semigroups S, we also investigate the projectivity of c0(S). We prove that for many semigroups S for which the Banach algebra ?1(S) is non-amenable, the ?1(S)-module ?1(S) is not injective. The main result about the projectivity of c0(S) states that for a weakly cancellative inverse semigroup S, c0(S) is projective if and only if S is finite. 相似文献
16.
17.
The community structure has been empirically found in many real networks. This paper proposes an efficient Double Shortest Path routing strategy trying to avoid the modules of traffic congestion, which means that we adopt the shortest routing strategy both in the inter-modules and in the intra-module. Simulations show that this routing algorithm is superior to the traditional shortest path routing protocol with appropriate selection of the tunable parameters. In addition, this algorithm can also be improved by integrating it with several alternative routing strategies. 相似文献
18.
Zeng Guangxing 《代数通讯》2013,41(10):3052-3063
The purpose of this article is to introduce the notion of real valuations on modules over commutative rings. These real valuations are characterized by their associated valuation triples, and a necessary and sufficient condition for a module to possess a real valuation is established. Moreover, the close interplay between valuations and orderings on a module is investigated by introducing the compatibility of valuations with orderings. Via the compatibility of valuations with orderings, the reality of valuations on a module also is characterized. 相似文献
19.
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
20.
Katherine Pinzon 《代数通讯》2013,41(6):2186-2194
Absolutely pure modules act in ways similar to injective modules. There are conditions on a ring which guarantee that the class of injective modules will be covering. In this article, we define conditions on the ring R which guarantee that the class of absolutely pure modules will be covering. These include R being left coherent, which we show implies a number of other necessary properties. 相似文献