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1.
伪补分配格上的主同余关系 总被引:7,自引:0,他引:7
本文研究了伪补分配格L的*-同余关系的基本性质。主要给出了:⑴主同余θ*(a,b)的一个具体刻划;⑵理想Ⅰ成为同余理想的一个充要条件的以Ⅰ为核心的最小*-同余θ*(I);⑶L上的格同余θL(a,b)成为*-同余的干充要条件。其中的大部分结果必进或包含了已有的结论。 相似文献
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设T(X, Y,θ)是两个非空集合X, Y上的夹心半群,其中θ是从Y到X的一个映射.本文刻画了这个半群T(X, Y,θ)上的一些同余,得到了半群上的同余链. 相似文献
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罗从文 《纯粹数学与应用数学》1998,14(4):7-10
以弱射影为工具,得到了DeMorgan代数的主同余关系的刻划,在此基础上证明了同余格θ(L)为原子的充要条件是L为弱原子的。然后通过引进极小商的概念,描述了θ(L)是布尔格的De Morgan代数L。 相似文献
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伪补分配格的同余理想与同余关系 总被引:5,自引:1,他引:4
王尊全 《纯粹数学与应用数学》2001,17(4):363-367
L是完备的伪补分配格,I是L的同余理想,本文得到以下结果:⑴θ是L的以I为核的最大同余关系的条件。⑵L的以I为核的同余关系是唯一的充分必要条件。⑶L的同余理想与同余关系之间有一一对应关系的充分必要条件。 相似文献
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一次同余方程的求解技巧 总被引:1,自引:0,他引:1
1 引言一次同余方程形如ax≡ b( mod m) ( 1 )其中 a,b,m都是整数 ,m≠ 0 ,m|a。一次同余方程 ( 1 )有解的充要条件是( a,m) |b ( 2 )当条件 ( 2 )满足时 ,一次同余方程 ( 1 )一共有 ( a,m)个解。并且 ,如果 x0 是 ( 1 )的某一特解 ,则 ( 1 )的全部解是 [1]x =x0 +m( a,m) t( mod m) , ( 3 )其中 t=0 ,1 ,… ,( a,m) -1。因此 ,当一次同余方程有解并且有不只一个解时 ,关键是求出它的一个特解。设 ( a,m) =g,a=a1g,b=b1g,m=m1g则必有 ( a1,m1) =1。此时可以取一次同余方程a1x≡ b1( mod m1) ( 4)的唯一解做 ( 1 )的一个特解 [1]。问题是 ,… 相似文献
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设k≥2,Hk表示一个正整数n的集合,使对任意的正整数q,同余方程a+b2三n(modq)在模q的既约剩余系中有解a,b.Dk(N)表示n≤N,n∈Hk,但不能表成p1+p22=n的数的个数,其中p1,p2表示素数.则在GRH下,Dk(N)<<N1-1/k(h(k)+1)+ε,这里k=2,3;h(2)=2,h(3)=8. 相似文献
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For varieties of algebras, we present the property of having "definable principal subcongruences" (DPSC), generalizing the
concept of having definable principal congruences. It is shown that if a locally finite variety V of finite type has DPSC, then V has a finite equational basis if and only if its class of subdirectly irreducible members is finitely axiomatizable. As an
application, we prove that if A is a finite algebra of finite type whose variety V(A) is congruence distributive, then V(A) has DPSC. Thus we obtain a new proof of the finite basis theorem for such varieties. In contrast, it is shown that the group
variety V(S
3
) does not have DPSC.
Received May 9 2000; accepted in final form April 26, 2001. 相似文献
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罗从文 《数学物理学报(B辑英文版)》2008,28(2):315-320
In this article, for any a in the MS-algebra L, the author considers the con- gruence of the form defined by (x,y) ∈θa→←x∧a°° = y ∧a° and x ∨ a°° = y ∨ a°°. A characterization of subdirectly irreducible MS-algebras is given and it is also proved that the union of two principal congruences having this form is a principal congruence if and only if L ∈ K2 ∨ K3. 相似文献
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Congruence subgroups of Hecke groups 总被引:1,自引:0,他引:1
Hecke groups are an important tool in subgroups of Hecke groups play an important rule investigating functional equations, and congruence in research of the solutions of the Dirichlet series. When q, m are two primes, congruence subgroups and the principal congruence subgroups of level m of the Hecke group H(√q) have been investigated in many papers. In this paper, we generalize these results to the case where q is a positive integer with q ≥ 5, √q ¢ Z and m is a power of an odd prime. 相似文献
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In this paper, we prove that every lattice L has a congruence-preserving extension into a regular lattice , moreover, every compact congruence of is principal. We construct by iterating a construction of the first author and F. Wehrung and taking direct limits.? We also discuss the case of a finite
lattice L, in which case can be chosen to be finite, and of a lattice L with zero, in which case can be chosen to have zero and the extension can be chosen to preserve zero.
Received September 10, 1999; accepted in final form October 16, 2000. 相似文献
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For a complete lattice C, we consider the problem of establishing when the complete lattice of complete congruence relations on C is a complete sublattice of the complete lattices of join- or meet-complete congruence relations on C. We first argue that this problem is not trivial, and then we show that it admits an affirmative answer whenever C is continuous for the join case and, dually, co-continuous for the meet case. As a consequence, we prove that if C is continuous then each principal filter generated by a continuous complete congruence on C is pseudocomplemented.
Received January 6, 1998; accepted in final form July 2, 1998. 相似文献
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Kilp and Knauer in(Comm. Algebra, 1992, 20(7), 1841–1856) gave characterizations of monoids when all generators in category of right S-acts(S is a monoid) satisfy properties such as freeness, projectivity, strong flatness, Condition(P), principal weak flatness, principal weak injectivity, weak injectivity, injectivity, divisibility, strong faithfulness and torsion freeness.Sedaghtjoo in(Semigroup Forum, 2013, 87: 653–662) characterized monoids by some other properties of generators including weak flatness, Condition(E) and regularity. To our knowledge,the problem has not been studied for properties mentioned above of(finitely generated, cyclic,monocyclic, Rees factor) right acts. In this article we answer the question corresponding to these properties and also f g-weak injectivity. 相似文献
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A characterization of principal congruences of the subvariety C of semi-DeMorgan algebras is given. This characterization is applied to determine the subdirectly irreducible algebras of
the variety C and to describe a poset such that the lattice of its order ideals is isomorphic to the lattice of subvarieties of C.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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纯正半群上的同余扩张(一) 总被引:1,自引:1,他引:0
刻划半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题.本文讨论了带上的同余的正规性和不变性以及在其Hall半群上的扩张,从同余扩张的角度刻划了带上的同余的性质,给出了扩张的极大、极小同余的描述. 相似文献
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Recep Sahin 《Applied mathematics and computation》2011,218(3):1025-1029
In this paper, we give the group structures and the signatures of some normal subgroups of the extended modular group Π containing the principal congruence subgroup Γ(12). 相似文献