共查询到20条相似文献,搜索用时 15 毫秒
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A. G. Pinus 《Siberian Mathematical Journal》2006,47(4):714-719
We prove some representation theorems for lattices and their lower subsemilattices as the lattices of congruences and subsemilattices of first-order definable congruences of universal algebras. 相似文献
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引入了左富足半群上fuzzy右好同余和fuzzy右消去同余的概念,给出了左富足半群上fuzzy右好同余的性质和特征.在此基础上,给出了左型A半群上fuzzy右好同余和fuzzy右消去同余的性质.得到了左型A半群上的fuzzy右好同余为fuzzy右消去同余的充要条件. 相似文献
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Françoise Reynaud 《Discrete Mathematics》1975,12(1):37-53
The paper deals with tournaments (i.e., with trichotomic relations) and their homomorphisms. The study of tournaments by means of their homomorphisms is natural as tournaments are algebras of a special kind. We prove (1) theorems which relate combinatorial and algebraic notions (e.g., the score of a tournament and the monoid of its endomorphisms); (2) theorems concerned with strictly algebraic aspects of tournaments (e.g., characterizing the lattice of congruences of a tournament). Our main result is that the group of automorphisms and the lattice of congruences of a tournament are in general independent. In the last part of the paper we give some examples and applications to other fields. 相似文献
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Wells Johnson 《Journal of Number Theory》1975,7(2):251-265
Many of the classical theorems for the Bernoulli numbers, particularly those congruences needed in the study of irregular primes, follow easily from the existence of the (p ? 1)st roots of unity in the ring of p-adic integers. Proofs are given for the von Staudt-Clausen theorem, the theorem of J. C. Adams, the Friedmann-Tamarkine congruence, a theorem of Vandiver, special cases of the congruences of Voronoi, Kummer, and Carlitz, and the congruences of E. Lehmer. 相似文献
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It is well known that the smallest semilattice congruence can be described via filters. We generalise this result to the smallest
left (right) normal band congruences and also to arbitrary semilattice (left normal band, right normal band) congruences,
describing them all via filters. To achieve this, we introduce filters relative to arbitrary quasiorders on a semigroup (traditional
filters are filters relative to the smallest negative operation-compatible quasiorder). We study congruences which can be
described via filters. We show that the lattice of semilattice (left normal band, right normal band) congruences is a homomorphic
image of the lattice of negative (right negative, left negative) operation-compatible quasiorders. 相似文献
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Some theorems for the null conguences within the framework of general theory of relativity are given. These theorems are important in themselves as they illustrate the geometric meaning of the spin coefficients. The newly developed Geroch-Held-Penrose (GHP) formalism has been used throughout the investigations. The salient features of GHP formalism that are necessary for the present work are given, and these techniques are applied to a pair of null congruences C (l) and C(n). 相似文献
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Analogs of some classical theorems on commuting matrices are proved. The new theorems deal with unitary congruences rather
than unitary similarities; commutation is replaced by concommutation, defined in the paper, whereas normal and Hermitian matrices
are replaced by conjugate-normal and symmetric matrices, respectively. Bibliography: 5 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 346, 2007, pp. 49–62. 相似文献
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We discuss some types of congruences on Menger algebras of rank n, which are generalizations of the principal left and right congruences on semigroups. We also study congruences admitting various types of cancellations and describe their relationship with strong subsets. 相似文献
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《International Journal of Approximate Reasoning》2009,50(3):623-630
In rough set theory, attribute reduction is an important mechanism for knowledge discovery. This paper mainly deals with attribute reductions of an inconsistent decision information system based on a dependence space. Through the concept of inclusion degree, a generalized decision distribution function is first constructed. A decision distribution relation is then defined. On the basis of this decision distribution relation, a dependence space is proposed, and an equivalence congruence based on the indiscernibility attribute sets is also obtained. Applying the congruences on a dependence space, new approaches to find a distribution consistent set are formulated. The judgement theorems for judging distribution consistent sets are also established by using these congruences and the decision distribution relation. 相似文献
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《Differential Geometry and its Applications》1999,10(1):1-26
The space of lines in R3 can be viewed as a four dimensional homogeneous space of the group of Euclidean motions, E(3). Line congruences arise in the classical method of transforming one surface to another by lines. These transformations are particularly interesting if some geometric property of the original surface is preserved. Line congruences, then, are two parameter families of lines and can be studied as surfaces in the space of lines. In this paper, we use the method of moving frames to study line congruences. We calculate the first order invariants of line congruences for which there are two real focal surfaces, and give the geometric meaning of these invariants. We look specifically at the case where the two first order invariants are constant and give a simple proof of Bäcklund's Theorem which relates to the transformation of one pseudospherical surface, a surface of constant negative Gaussian curvature, to another. These transformations are of interest since pseudospherical surfaces correspond to solutions to the sine-Gordon equation. We also give a proof of Bianchi's permutability theorem for pseudospherical surfaces in this context. Finally, we use the results of these theorems to generate some pseudospherical surfaces. All of these concepts and results are understood in terms of the structure equations of the line congruence. 相似文献
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半环R被称为实半环,若对于任意的n∈N,方程x1^2+…+xn^2=0在R中只有零解:x1=…=xn=0.为了刻画实半环,引入了实理想和极小素理想的概念,利用同余的方法,得到了可减半环类中实半环的结构定理. 相似文献
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Dinesh S. Thakur 《Finite Fields and Their Applications》2012,18(2):271-282
We present several elementary theorems, observations and questions related to the theme of congruences satisfied by binomial coefficients and factorials modulo primes (or prime powers) in the setting of polynomial ring over a finite field. When we look at the factorial of n or the binomial coefficient ‘n choose m’ in this setting, though the values are in a function field, n and m can be usual integers, polynomials or mixed. Thus there are several interesting analogs of the well-known theorems of Lucas, Wilson etc. with quite different proofs and new phenomena. 相似文献
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Robert H. Oehmke 《Journal of Applied Mathematics and Computing》1998,5(3):475-480
In a number of earlier papers the study of the structure of semigroups has been approached by means of right congruences. Such an approach seems appropriate since a right congruence is one of the possible analogs of both the right ideal of a ring and the subgroup in a group. Each of these substructures plays a strong role in the study of the structure of their respective systems. In both the ring and the group the internal direct product is naturally, and effectively, defined. However, what such an internal direct product should be for two right congruences of a semigroup is not so clear. In this paper we will offer a possible definition and consider some of the consequences of it. We will also extend some of these results to automata. 相似文献
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Chong-Yih Wu 《Semigroup Forum》2012,85(2):369-380
A right congruence ?? in a semigroup S is essential if for any right congruence ?? we have ??????=?? (the identity relation) implies ??=??. Clearly, the universal relation, ??, is an essential right congruence. We say ?? is proper if ??????. In this paper we get a necessary and sufficient condition for a semigroup with an identity element?1 and having no proper essential right congruences to have a distributive lattice of right congruences. 相似文献
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Chin-Hong Park 《Semigroup Forum》1994,48(1):263-271
LetA=(M, S, δ) be an automaton without outputs whereM is a nonemptyset andS is a nonempty semigroup. Then the right congruences μM and μ m associated withS have been expressed in many different ways (μ M is called the Myhill-Nerode congruence onS). Also, their algebraic properties have been investigated. We have introduced the right congruences μ S and μα onM and we have obtained necessary and sufficient conditions thatS/μ andM/w have nontrivialS-homomorphisms where μ andw are any right congruences onS andM respectively. The faithfulness ofS has been introduced. 相似文献
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Istkhar Ali 《Journal of Applied Mathematics and Computing》2018,58(1-2):323-334
In this paper, localization theorems for left and right eigenvalues of a quaternion matrix are presented. Some differences between quaternion matrices and split quaternion matrices are summarized. A counter example for Gerschgorin theorems for left and right eigenvalues of a split quaternion matrix is given. Finally, a method for finding right eigenvalues of a split quaternion matrix pencil is presented. 相似文献
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William J. Keith 《The Ramanujan Journal》2016,40(1):71-92
We generalize overpartitions to (k, j)-colored partitions: k-colored partitions in which each part size may have at most j colors. We find numerous congruences and other symmetries. We use a wide array of tools to prove our theorems: generating function dissections, modular forms, bijections, and other combinatorial maps. In the process of proving certain congruences, we find results of independent interest on the number of partitions with exactly 2 sizes of part in several arithmetic progressions. We find connections to divisor sums, the Han/Nekrasov–Okounkov hook length formula and a possible approach to finitization, and other topics, suggesting that a rich mine of results is available. We pose several immediate questions and conjectures. 相似文献
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设S是有向序半群,本文给出了S上的一类正则同余,称为强序同余的定义及性质.证明了S的强序同余是强正则同余,但反之不成立.同时证明了强序同余格SOC(S)是S的同余格C(S)关于通常集合的交和传递积的V-完备的分配子格. 相似文献
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An Invitation to C-semigroups 总被引:1,自引:0,他引:1