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1.
V. V. Bludov 《Algebra and Logic》2002,41(1):1-7
We construct an example of a 2-generated group G and describe a set of proper maximal subquasivarieties in the quasivariety qG. This set proves to be infinite, which gives an affirmative answer to Question 14.25 posed by A. I. Budkin in the Kourovka Notebook. Moreover, it is shown that every proper subquasivariety in qG is contained in a proper maximal one. 相似文献
2.
We consider the question of preservation of universal equivalence for the cartesian and direct wreath products of lattice-ordered groups and groups. We prove that the basic rank is infinite of the quasivariety of torsion-free nilpotent groups of nilpotence length c (c2) 相似文献
3.
M. V. Volkov 《Algebra Universalis》2001,46(1-2):97-103
No Abstract. Received January 2, 2000; accepted in final form August 28, 2000. 相似文献
4.
The classical Glivenko theorem asserts that a propositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK‐logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK‐logic with negation by a family of connectives implicitly defined by equations and compatible with BCK‐congruences. Many of the logics in the current literature are natural expansions of BCK‐logic with negation. The validity of the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one‐variable formula in the language of BCK‐logic with negation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Projectively condensed semigroups,generalized completely regular semigroups and projective orthomonoids 总被引:1,自引:0,他引:1
The class of projectively condensed semigroups is a quasivariety of unary semigroups, the class of projective orthomonoids is a subquasivariety
of . Some well-known classes of generalized completely regular semigroups will be regarded as subquasivarieties of . We give the structure semilattice composition and the standard representation of projective orthomonoids, and then obtain
the structure theorems of various generalized orthogroups.
Partially supported by a UGC (HK) grant #2060123 (04-05). 相似文献
6.
We suggest an algebraic approach to the study of colour-families of graphs. This approach is based on the notion of a congruence
of an arbitrary structure. We prove that every colour-family of graphs is a finitely generated universal Horn class and show
that for every colour-family the universal theory is decidable. We study the structure of the lattice of colour-families of
graphs and the lattice of antivarieties of graphs. We also consider bases of quasi-identities and bases of anti-identities
for colour-families and find certain relations between the existence of bases of a special form and problems in graph theory.
Received January 19, 1999; accepted in final form October 25, 1999. 相似文献
7.
Denote by Υ1 the collection of quasivarieties of pseudo-MV-algebras; and by Υ2, the collection of quasivarieties of lattice-ordered groups. With respect to the set-theoretic inclusion, Υ1 and Υ2 are lattices. We note some properties of Υ1 and construct an injective mapping φ of Υ2 into Υ1 such that Z 1?Z 2??(Z 1)??(Z 2) for all Z 1, Z 2 ∈ Υ2. 相似文献
8.
A. I. Budkin 《Algebra and Logic》2007,46(4):219-230
Let Lq(qG) be the quasivariety lattice contained in a quasivariety generated by a group G. It is proved that if G is a finitely
generated torsion-free group in
(i.e., G is an extension of an Abelian group by a group of exponent 2n), which is a split extension of an Abelian group by a cyclic group, then the lattice Lq(qG) is a finite chain.
__________
Translated from Algebra i Logika, Vol. 46, No. 4, pp. 407–427, July–August, 2007. 相似文献
9.
S. A. Shakhova 《Algebra and Logic》2005,44(2):132-139
Let M be any quasivariety of Abelian groups,
(H) be the dominion of a subgroup H of a group G in M, and Lq(M) be the lattice of subquasivarieties of M. It is proved that
(H ) coincides with a least normal subgroup of the group G containing H, the factor group with respect to which is in M. Conditions are specified subject to which the set L(G,H,M) = {
(H) | N Lq(M)} forms a lattice under set-theoretic inclusion and the map : Lq(M) L(G,H,M) such that (N) =
(H) for any quasivariety N Lq(M)is an antihomomorphism of the lattice L
q
(M) onto the lattice L(G, H, M).__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 238–251, March–April, 2005. 相似文献
10.
V. A. Khudyakov 《Algebra and Logic》2003,42(6):419-427
We introduce concepts of a continuous family of quasi-identities and of a continuous quasivariety. For continuous quasivarieties, a characterization theorem and an analog of the Birkhoff theorem on subdirect decomposition are proved. Also we point out the way of constructing examples of continuous quasivarieties and furnish the characterization of a relative congruence lattice of systems in the quasivarieties in question. Lastly, we re-prove the Hahn–Banach theorem on extension of a linear functional. 相似文献