共查询到20条相似文献,搜索用时 15 毫秒
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This research was done during the second aurthor's stay in National Cheng-Kung University, Tainan. Support by the grant No. VRP92034 from the National Science Council of ROC is gratefully acknowledged. 相似文献
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Dedicated to Bjarni Jónsson on the occasion of his 70th birthday 相似文献
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K.A. Kearnes 《Algebra Universalis》1999,42(3):165-181
Let A be a finite algebra that generates a congruence modular variety. We show that the free spectrum of V(A){\cal V}({\bf A}) fails to have a doubly exponentially lower bound if and only if A has a finitely generated clone and A is a direct product of nilpotent algebras of prime power cardinality. 相似文献
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Pawel M. Idziak 《Algebra Universalis》1988,25(1):365-383
The aim of this paper is to prove that every finitely generated, arithmetical variety of finite type, in which every subdirectly irreducible algebra has linearly ordered congruences has a decidable first order theory of its finite members. The proof is based on a representation of finite algebras from such varieties by some quotients of special subdirect products in which sets of indices are partially ordered into dual trees. Then the result of M. O. Rabin about decidability of the monadic second order theory of two successors is applied.Presented by Stanley Burris. 相似文献
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Emil W. Kiss 《Algebra Universalis》1985,21(2-3):213-224
We present an algorithm that, given a finite algebraA generating a congruence distributive (CD) variety, determines whether this variety has first order definable principal congruences (DPC). In fact, DPC turns out to be equivalent to the extendability of the principal congruences of certain subalgebras of the algebras in HS(A
3). To verify this algorithm, we investigate combinatorial properties of finite subdirect powers ofA. Our theorem has a relatively simple formulation for arithmetical algebras. As an application, we obtain McKenzie's result that there are no nondistributive lattice varieties with DPC.Presented by A. Pixley.Finally I wish to thank E. Fried, R. W. Quackenbush and P. Pröhle for many helpful conversations (some ideas of the paper came up by considering weakly associative lattices), and to A. F. Pixley for raising the problem mentioned in the first section, which was the starting point of this investigation. 相似文献
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Ralph McKenzie 《Algebra Universalis》1991,28(4):589-603
We prove that in a locally finite variety with the congruence extension property, locally solvable congruences are central and locally solvable algebras are Hamiltonian. Also, we prove that a maximal subuniverse of a finite algebra in an Abelian variety is identical with an equivalence class of some congruence.Presented by H. P. Gumm. 相似文献
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We provide several conditions that, among locally finite varieties, characterize congruence meet-semidistributivity and we use these conditions to give a new proof of a finite basis theorem published by Baker, McNulty, and Wang in 2004. This finite basis theorem extends Willard’s Finite Basis Theorem. 相似文献
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Norman R. Reilly 《Semigroup Forum》2013,86(1):162-182
In a previous paper, the author showed how to associate a completely 0-simple semigroup with a connected bipartite graph containing labelled edges. In the main theorem, it is shown how these fundamental semigroups can be used to describe the regular principal factors of the free objects in certain Rees-Sushkevich varieties, namely, the varieties of semigroups that are generated by all completely 0-simple semigroups over groups in a variety of finite exponent. This approach is then used to solve the word problem for each of these varieties for which the corresponding group variety has solvable word problem. 相似文献
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Definable principal congruences in varieties of groups and rings 总被引:1,自引:0,他引:1
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Congruence properties in congruence permutable and in ideal determined varieties, with applications.
C. J. van. Alten 《Algebra Universalis》2005,53(4):433-449
We define a weak version of EDPC (equationally definable principal congruences), called EDPC*, that is shown to be preserved under varietal closure in congruence permutable varieties. We show that if
is a congruence permutable variety generated by a class
then
has EDPC iff
has EDPC* iff
has EDPC*. An equational condition is given which, if satisfied by
implies that
has the CEP (congruence extension property). Similar results are proved for ideal determined varieties. These results are applied to the variety of residuated lattices, with examples.Received January 15, 2004; accepted in final form October 8, 2004. 相似文献
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This paper deals with notions of (equational) definability of principal ideals in subtractive varieties. These notions are
first characterized in several different ways. The strongest notion (EDPI) is then further investigated. We introduce the
variety of MINI algebras (a generalization of Hilbert algebras) and we show that they are a paradigm for subtractive EDPI varieties. Finally we deal
with principal ideal operations, and in particular with the cases of meet and join of principal ideals being equationally
definable.
Received November 7, 1996; accepted in final form December 17, 1997. 相似文献