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1.
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
2.
Be’eri Greenfeld 《代数通讯》2017,45(11):4783-4784
We construct a ring which admits a 2-generated, faithful torsion module but lacks a cyclic faithful torsion module. This answers a question by Oman and Schwiebert [1, 2]. 相似文献
3.
In [1], Bannai presents a fusion condition and uses this to consider central Schur rings (S-rings) over the simple groups PSL(2,q) where q is a prime power. In this paper, we concretely describe all such S-rings in terms of symmetric S-rings over cyclic groups. The final section discusses counting these. 相似文献
4.
《Optimization》2012,61(3):675-686
AbstractIn this paper, we characterize two power indices introduced in [1] using two different modifications of the monotonicity property first stated by [2]. The sets of properties are easily comparable among them and with previous characterizations of other power indices. 相似文献
5.
Elisabeth Remm 《代数通讯》2017,45(7):2956-2966
The notion of breadth of a nilpotent Lie algebra was introduced and used to approach problems of classification up to isomorphism in [5]. In the present paper, we study this invariant in terms of characteristic sequence, another invariant, introduced by Goze and Ancochea in [1]. This permits to complete the determination of Lie algebras of breadth 2 studied in [5] and to begin the work for Lie algebras with breadth greater than 2. 相似文献
6.
Yong Kong 《Journal of Difference Equations and Applications》2013,19(15):1265-1271
The Goulden–Jackson cluster method is a powerful method to find generating functions of pattern occurrences in random sequences [1]. The method is clearly explained, extended and implemented by Noonan and Zeilberger [2]. In this paper, we elaborate on one of the several extensions in [2], namely the extension from symmetrical Bernoulli sequences where the occurrences of each symbol have equal probability, to asymmetrical Bernoulli sequences with different probabilities of symbol generations. An explicit formula is derived for the extension, which is implicitly embedded in the treatment of [2]. The extended result is then compared with the method of Régnier–Szpankowski [3], a method which was developed independently to tackle the same problem. By manipulating some matrix inversions, we show that the Régnier–Szpankowski method can be simplified to the extended Goulden–Jackson method. 相似文献
7.
Stéphane Launois 《代数通讯》2017,45(3):1294-1313
Cauchon [5] introduced the so-called deleting derivations algorithm. This algorithm was first used in noncommutative algebra to prove catenarity in generic quantum matrices, and then to show that torus-invariant primes in these algebras are generated by quantum minors. Since then this algorithm has been used in various contexts. In particular, the matrix version makes a bridge between torus-invariant primes in generic quantum matrices, torus orbits of symplectic leaves in matrix Poisson varieties and totally non-negative cells in totally non-negative matrix varieties [12]. This led to recent progress in the study of totally non-negative matrices such as new recognition tests [18]. The aim of this article is to develop a Poisson version of the deleting derivations algorithm to study the Poisson spectra of the members of a class 𝒫 of polynomial Poisson algebras. It has recently been shown that the Poisson Dixmier–Moeglin equivalence does not hold for all polynomial Poisson algebras [2]. Our algorithm allows us to prove this equivalence for a significant class of Poisson algebras, when the base field is of characteristic zero. Finally, using our deleting derivations algorithm, we compare topologically spectra of quantum matrices with Poisson spectra of matrix Poisson varieties. 相似文献
8.
9.
The article deals with a fluid dynamic model for traffic flow on a road network. This consists of a hyperbolic system of two equations proposed in Aw and Rascle (2000). A method to solve Riemann problems at junctions is given assigning rules on traffic distributions and maximizations of fluxes and other quantities. Then we discuss stability in L ∞ norm of such solutions. Finally, we prove existence of entropic solutions to the Cauchy problem when the road network has only one junction. 相似文献
10.
Thomas Laurent 《偏微分方程通讯》2013,38(12):1941-1964
The purpose of this work is to develop a satisfactory existence theory for a general class of aggregation equations. An aggregation equation is a non-linear, non-local partial differential equation that is a regularization of a backward diffusion process. The non-locality arises via convolution with a potential. Depending on how regular the potential is, we prove either local or global existence for the solutions. Aggregation equations have been used recently to model the dynamics of populations in which the individuals attract each other (Bodnar and Velazquez, 2005; Holm and Putkaradze, 2005; Mogilner and Edelstein-Keshet, 1999; Morale et al., 2005; Topaz and Bertozzi, 2004; Topaz et al., 2006). 相似文献
11.
In this article we prove a few interesting properties of just infinite algebras. Bartholdi (2006), defines a particular class of just infinite algebras and demonstrates various properties of these examples. One such property, which is tedious to prove for his specific examples, is primality. We prove here that, in fact, all just infinite algebras are prime. We then consider two corollaries of this theorem; one suggests a weaker definition of just infinite for finitely generated algebras and the other examines the specific case of just infinite algebras which also satisfy a polynomial identity. 相似文献
12.
Eskandar Naraghirad 《Numerical Functional Analysis & Optimization》2017,38(4):409-426
In this article, using Bregman functions and Bregman distances, we first introduce the notion of Bregman best proximity points, extending the notion of best proximity points introduced and studied in [1]. We then prove existence and convergence results of Bregman best proximity points for Bregman cyclic contraction mappings in the setting of Banach spaces. It is well known that the Bregman distance does not satisfy either the symmetry property or the triangle inequality which are required for standard distances. Numerical examples are included at the end of the paper. So, our results improve and generalize many known results in the current literature. 相似文献
13.
ABSTRACT We study self-dual coradically graded pointed Hopf algebras with a help of the dual Gabriel theorem for pointed Hopf algebras (van Oystaeyen and Zhang, 2004). The co-Gabriel Quivers of such Hopf algebras are said to be self-dual. An explicit classification of self-dual Hopf quivers is obtained. We also prove that finite dimensional pointed Hopf algebras with self-dual graded versions are generated by group-like and skew-primitive elements as associative algebras. This partially justifies a conjecture of Andruskiewitsch and Schneider (2000) and may help to classify finite dimensional self-dual coradically graded pointed Hopf algebras. 相似文献
14.
The Bose–Mesner algebra of the association scheme of the ordinary n-gon has the following remarkable properties:
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(i) It has a P-polynomial structure with respect to every faithful basis element; and
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(ii) Any closed subset generated by a basis element has a P-polynomial structure with respect to this basis element.
15.
The pioneering work of Brezis-Merle [7], Li-Shafrir [27], Li [26], and Bartolucci-Tarantello [3] showed that any sequence of blow-up solutions for (singular) mean field equations of Liouville type must exhibit a “mass concentration” property. A typical situation of blowup occurs when we let the singular (vortex) points involved in the equation (see (1.1) below) collapse together. However in this case, Lin-Tarantello in [30] pointed out that the phenomenon: “bubbling implies mass concentration” might not occur and new scenarios open for investigation. In this paper, we present two explicit examples which illustrate (with mathematical rigor) how a “nonconcentration” situation does happen and its new features. Among other facts, we show that in certain situations, the collapsing rate of the singularities can be used as blow-up parameter to describe the bubbling properties of the solution-sequence. In this way, we are able to establish accurate estimates around the blow-up points which we hope to use toward a degree counting formula for the shadow system (1.34) below. 相似文献
16.
Victor Petrogradsky 《代数通讯》2017,45(7):2912-2941
The Grigorchuk and Gupta-Sidki groups play fundamental role in modern group theory. They are natural examples of self-similar finitely generated periodic groups. The author constructed their analogue in case of restricted Lie algebras of characteristic 2 [27], Shestakov and Zelmanov extended this construction to an arbitrary positive characteristic [39]. There are a few more examples of self-similar finitely generated restricted Lie algebras with a nil p-mapping, but, as a rule, that algebras have no clear basis and require technical computations. Now we construct a family L(Ξ) of 2-generated restricted Lie algebras of slow polynomial growth with a nil p-mapping, where a field of positive characteristic is arbitrary and Ξ an infinite tuple of positive integers. Namely, GKdimL(Ξ)≤2 for all such algebras. The algebras are constructed in terms of derivations of infinite divided power algebra Ω. We also study their associative hulls A?End(Ω). Algebras L and A are ?2-graded by a multidegree in the generators. If Ξ is periodic then L(Ξ) is self-similar. As a particular case, we construct a continuum subfamily of non-isomorphic nil restricted Lie algebras L(Ξα), α∈?+, with extremely slow growth. Namely, they have Gelfand-Kirillov dimension one but the growth is not linear. For this subfamily, the associative hulls A have Gelfand-Kirillov dimension two but the growth is not quadratic. The virtue of the present examples is that they have clear monomial bases. 相似文献
17.
We propose a level set method for systems of PDEs which is consistent with the previous research pursued by Evans (1996) for the heat equation and by Giga and Sato (2001) for Hamilton–Jacobi equations. Our approach follows a geometric construction related to the notion of barriers introduced by De Giorgi. The main idea is to force a comparison principle between manifolds of different codimension and require each nonzero sub-level of a solution of the level set equation to be a barrier for the graph of a solution of the corresponding system. We apply the method to a class of systems of first order quasi-linear equations. We compute the level set equation associated with suitable first order systems of conservation laws, with the mean curvature flow of a manifold of arbitrary codimension and with systems of reaction–diffusion equations. 相似文献
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19.
Héctor Suárez 《代数通讯》2017,45(10):4569-4580
Pre-Koszul and Koszul algebras were defined by Priddy [15]. There exist some relations between these algebras and the skew PBW extensions defined in [8]. In [24] we gave conditions to guarantee that skew PBW extensions over fields it turns out homogeneous pre-Koszul or Koszul algebra. In this paper we complement these results defining graded skew PBW extensions and showing that if R is a finite presented Koszul 𝕂-algebra then every graded skew PBW extension of R is Koszul. 相似文献
20.
Romain Gicquaud 《偏微分方程通讯》2013,38(8):1313-1367
In this paper we pursue the work initiated in [6, 7]: study the extent to which conformally compact asymptotically hyperbolic metrics can be characterized intrinsically. We show how the decay rate of the sectional curvature to ?1 controls the Hölder regularity of the compactified metric. To this end, we construct harmonic coordinates that satisfy some Neumann-type condition at infinity. Combined with a new integration argument, this permits us to recover to a large extent our previous result without any decay assumption on the covariant derivatives of the Riemann tensor. 相似文献