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It is known that the semigroup Sing n of all singular self-maps of X n = {1,2,…, n} has rank n(n ? 1)/2. The idempotent rank, defined as the smallest number of idempotents generating Sing n , has the same value as the rank. (See Gomes and Howie, 1987.) Idempotents generating Sing n can be seen as special cases (with m = r = 2) of (m, r)-path-cycles, as defined in Ay\i k et al. (2005). The object of this article is to show that, for fixed m and r, the (m, r)-rank of Sing n , defined as the smallest number of (m, r)-path-cycles generating Sing n , is once again n(n ? 1)/2. 相似文献
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Jan Uliczka 《代数通讯》2013,41(10):3401-3409
In this note we want to generalize some of the results in [1] from polynomial rings in several indeterminates to arbitrary ? n -graded commutative rings. We will prove an analogue of Jaffard's Special Chain Theorem and a similar result for the height of a prime ideal 𝔭 over its graded core 𝔭*. 相似文献
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In this article we show, among others, that if R is a prime ring which is not a domain, then R is right nonsingular, right max-min CS with uniform right ideal if and only if R is left nonsingular, left max-min CS with uniform left ideal. The above result gives, in particular, Huynh et al. (2000) Theorem for prime rings of finite uniform dimension. 相似文献
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《代数通讯》2013,41(9):3179-3193
ABSTRACT If X and Y are sets, we let P(X, Y ) denote the set of all partial transformations from X into Y (that is, all mappings whose domain and range are subsets of X and Y, respectively). We define an operation * on P(X, Y ) by choosing θ ∈ P(Y, X) and writing: α*β = α °θ°β, for each α, β ∈ P(X, Y ). Then (P(X, Y ), *) is a semigroup, and some authors have determined when this is regular (Magill and Subbiah, 1975), when it contains a “proper dense subsemigroup” (Wasanawichit and Kemprasit, 2002) and when it is factorisable (Saengsura, 2001). In this paper, we extend the latter work to certain subsemigroups of (P(X, Y ), *). We also consider the corresponding idea for partial linear transformations from one vector space into another. In this way, we generalise known results for total transformations and for injective partial transformations between sets, and we establish new results for linear transformations between vector spaces. 相似文献
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Abdellatif Moudafi 《Numerical Functional Analysis & Optimization》2013,34(1):39-47
This article is concerned with a generalization of the hybrid steepest descent method from variational inequalities to the multivalued case. This will be reached by replacing the multivalued operator by its Yosida approximate, which is always Lipschitz continuous. It is worth mentioning that the hybrid steepest descent method is an algorithmic solution to variational inequality problems over the fixed point set of certain nonexpansive mappings and has remarkable applicability to the constrained nonlinear inverse problems like image recovery and MIMO communication systems (see, e.g., [9, 10]). 相似文献
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For a square-free monomial ideal I ? S = k[x 1, x 2,…, x n ], we introduce the notion of quasi-linear quotients. By using the quasi-linear quotients, we give a new algebraic criterion for the shellability of a pure simplicial complex Δ over [n]. Also, we provide a new criterion for the Cohen–Macaulayness of the face ring of a pure simplicial complex Δ. Moreover, we show that the face ring of the spanning simplicial complex (defined in [2]) of an r-cyclic graph is Cohen–Macaulay. 相似文献
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Mi Hee Park 《代数通讯》2013,41(4):1280-1292
Let R be an integral domain. A w-ideal I of R is called a w-multiplicative canonical ideal if (I: (I: J)) = J for each w-ideal J of R. In particular, if R is a w-multiplicative canonical ideal of R, then R is a w-divisorial domain. These are the w-analogues of the concepts of a multiplicative canonical ideal and a divisorial domain, respectively. Motivated by the articles [8, 10], we study the domains possessing w-multiplicative canonical ideals; in particular, we consider Prüfer v-multiplication domains. 相似文献
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Sei-Qwon Oh 《代数通讯》2017,45(1):76-104
A Poisson algebra ?[G] considered as a Poisson version of the twisted quantized coordinate ring ?q,p[G], constructed by Hodges et al. [11], is obtained and its Poisson structure is investigated. This establishes that all Poisson prime and primitive ideals of ?[G] are characterized. Further it is shown that ?[G] satisfies the Poisson Dixmier-Moeglin equivalence and that Zariski topology on the space of Poisson primitive ideals of ?[G] agrees with the quotient topology induced by the natural surjection from the maximal ideal space of ?[G] onto the Poisson primitive ideal space. 相似文献
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In this paper, we compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square path on n vertices. We also compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square cycle on n vertices, when n≡0,3,4( mod 5), and give tight bounds when n≡1,2( mod 5). We also prove a conjecture of Herzog presented in [5], for the edge ideals of square paths and square cycles. 相似文献
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We study the asymptotic behavior of solutions of the two dimensional incompressible Euler equations in the exterior of a curve when the curve shrinks to a point. This work links the two previous results [5, 9]. The second goal of this work is to complete the previous article, in defining the way the obstacles shrink to a curve. In particular, we give geometric properties for domain convergences in order that the limit flow be a solution of Euler equations. 相似文献
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Ryutaroh Matsumoto 《代数通讯》2013,41(1):401-405
In Hai and Thin [1], there is a theorem, stating that every locally nilpotent subnormal subgroup in a division ring D is central (see [1, Theoerem 2.2]). Unfortunately, there is some mistake in the proof of this theorem. In this note, we give the another proof of this theorem. 相似文献
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Samuel J. L. Kopamu 《代数通讯》2013,41(6):1852-1873
The skeleton of the lattice of all structurally trivial semigroup varieties is known to be isomorphic to an infinitely ascending inverted pyramid (Kopamu, 2003). We digitize the skeleton by representing each variety forming the skeleton as an ordered triple of non-negative integers. This digitization of the lattice, under the pointwise ordering of non-negative integers, provides useful algorithms which could easily be programmed into a computer, and then used to compute varietal joins and meets, or even to draw skeleton lattice diagrams. An application to a certain larger subvariety lattice is also given as an example. 相似文献
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A semigroup S is called F-monoid if S has an identity and if there exists a group congruence ρ on S such that each ρ-class of S contains a greatest element with respect to the natural partial order of S (see Mitsch, 1986). Generalizing results given in Giraldes et al. (2004) and specializing some of Giraldes et al. (Submitted) five characterizations of such monoids S are provided. Three unary operations “?”, “○”, and “ ? ” on S defined by means of the greatest elements in the different ρ-classes of S are studied. Using their properties a charaterization of F-monoids S by their regular part S° = {a°|a ? S} and the associates of elements in S° is given. Under the hypothesis that S ? = {a ?|a ? S} is a subsemigroup it is shown that S is regular, whence of a known structure (see Giraldes et al., 2004). 相似文献
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A. R. Aliabad 《代数通讯》2013,41(2):701-717
The theory of z-ideals and z°-ideals, especially as pertaining to the ideal theory of C(X), the ring of continuous functions on a completely regular Hausdorff space X, has been attended to during the recent years; see Gillman and Jerison [9], Mason [18], and Azarpanah et al. [4]. In this article we will consider the theory of z°-ideals as applied to the rings of polynomials over a commutative ring with identity. We introduce and study sz°-ideals (an ideal I of a ring is called sz°-ideal, if whenever S is a finite subset of I, then the intersection of all minimal prime ideals containing S is in I). In addition, we will pay attention to several annihilator conditions and find some new results. Finally, we use the two examples that appeared in Henriksen and Jerison [10] and Huckaba [12], to answer some natural questions that might arise in the literature. 相似文献
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We prove that there are no networks homeomorphic to the Greek “Theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees, such that under the motion by curvature they are self–similarly shrinking.This fact completes the classification of the self–similarly shrinking networks in the plane with at most two triple junctions, see [5, 10, 25, 2]. 相似文献
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Carmelo Antonio Finocchiaro 《代数通讯》2017,45(10):4521-4527
Using the general approach to invertibility for ideals in ring extensions given by Knebush and Zhang in [9], we investigate about connections between faithfully flatness and invertibility for ideals in rings with zero divisors. 相似文献