共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Given an ordered set P and an antitone map g : P P, we obtain necessary and sufficient conditions for the existence of an odd positive integer k such that gk is isotone. The results obtained have a natural application to the dual space of an Ockham algebra. In particular, we determine the cardinality of the endomorphism semigroup of a finite subdirectly irreducible Ockham algebra. 相似文献
3.
We show that every subdirectly irreducible Ockham chain belongs to the generalised variety K
ω and is countable. Consideration of three particular types of finite Ockham chains, together with their order duals, leads
to a determination of the structure of all finite subdirectly irreducible Ockham chains. These belong necessarily to the Berman
classes K
1,
q
and we show that there are precisely 6
q
+2 such chains in K
1,
q
. We also show that there are precisely 14 subdirectly irreducible Ockham chains whose endomorphism semigroup is regular,
such chains having at most 5 elements.
Received February 18, 1999; accepted in final form February 8, 2000. 相似文献
4.
引入一个具有Heyting结构Ockham代数,简称HO-代数.所谓HO-代数,是指具有(2,2,2,1,0,0)类型的代数(L;∧,∨,→,f,0,1).其中(L;f)是Ockham代数,(L;→)是Heyting代数,且运算f和→由恒等式f(x→y)=f^2(x)∧f(y)与f(x)→y=f^2(x)∨y所连结.主要讨论了HO-代数的同余关系的性质.并刻画了其次直不可约代数的某些性质. 相似文献
5.
6.
The variety pO consists of those algebras (L; ?, ?, f,*, 0,1) of type (2,2,1,1,0,0) where (L; ?, ?, f, 0,1) is an Ockham algebra, (Z; ?, ?,*, 0,1) is a p-algebra, and the unary operations f and * commute. We describe completely the structure of the subdirectly irreducible algebras that belong to the subclass pK1,1, characterised by the property f3 = f. 相似文献
7.
We show that every non-trivial subdirectly irreducible algebra in the variety generated by graph algebras is either a two-element
left zero semigroup or a graph algebra itself. We characterize all the subdirectly irreducible algebras in this variety. From
this we derive an example of a groupoid (graph algebra) that generates a variety with NP-complete membership problem. This
is an improvement over the result of Z. Székely who constructed an algebra with similar properties in the signature of two
binary operations.
The second author was supported by OTKA grants no. T043671, NK67867, K67870 and by NKTH (National Office for Research and
Technology, Hungary). 相似文献
8.
J. Ježek 《Czechoslovak Mathematical Journal》2004,54(1):229-231
The idempotent modification of a group is always a subdirectly irreducible algebra. 相似文献
9.
10.
讨论了分次环A,Ae和A#G*的相关性质,在A是分次忠实时,A#G*是亚直既约环当且仅当Ae是亚直既约环;在A是分次非退化时,A#G*是G亚直既约环当且仅当A是分次亚直既约环. 相似文献
11.
Fang Jie 《中国科学A辑(英文版)》2008,51(2):185-194
In this paper,we study a certain class of double Ockham algebras (L;∧,∨,f,k,0,1), namely the bounded distributive lattices (L;∧,∨,0,1) endowed with a commuting pair of unary op- erations f and k,both of which are dual endomorphisms.We characterize the subdirectly irreducible members,and also consider the special case when both (L;f) and (L;k) are de Morgan algebras.We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members, all of which are simple. 相似文献
12.
Peter Ouwehand 《Algebra Universalis》2013,69(3):201-211
This paper studies absolute retracts in congruence modular varieties of universal algebras. It is shown that every absolute retract with finite dimensional congruence lattice is a product of subdirectly irreducible algebras. Further, every absolute retract in a residually small variety is the product of an abelian algebra and a centerless algebra. 相似文献
13.
Subdirectly irreducible and free Kleene-Stone algebras 总被引:2,自引:0,他引:2
A Kleene-Stone algebra is a bounded distributive lattice with two unary operations that make it a Kleene and a Stone algebra. In this paper, we determine all subdirectly irreducible Kleene-Stone algebras, and describe the free Kleene-Stone algebra on a finite set of generators as a product of certain free Kleene algebras endowed with a Stone negation.Presented by J. Berman. 相似文献
14.
A nontrivial algebra with at least one at least binary operation is isomorphic to the factor of a subdirectly irreducible
algebra through its monolith if and only if the intersection of all its ideals is nonempty.
Received October 6, 2000; accepted in final form September 14, 2001. 相似文献
15.
Ján Jakubík 《Mathematica Slovaca》2010,60(2):189-194
The notion of idempotent modification of an algebra was introduced by Ježek; he proved that the idempotent modification of
a group is always subdirectly irreducible. In the present note we show that the idempotent modification of a generalized MV -algebra having more than two elements is directly irreducible if and only if there exists an element in A which fails to be boolean. Some further results on idempotent modifications are also proved. 相似文献
16.
17.
A near-Heyting algebra is a join-semilattice with a top element such that every principal upset is a Heyting algebra. We establish a one-to-one correspondence between the lattices of filters and congruences of a near-Heyting algebra. To attain this aim, we first show an embedding from the lattice of filters to the lattice of congruences of a distributive nearlattice. Then, we describe the subdirectly irreducible and simple near-Heyting algebras. Finally, we fully characterize the principal congruences of distributive nearlattices and near-Heyting algebras. We conclude that the varieties of distributive nearlattices and near-Heyting algebras have equationally definable principal congruences. 相似文献
18.
We investigate a construction of an integral residuated lattice starting from an integral residuated lattice and two sets with an injective mapping from one set into the second one. The resulting algebra has a shape of a Chinese cascade kite, therefore, we call this algebra simply a kite. We describe subdirectly irreducible kites and we classify them. We show that the variety of integral residuated lattices generated by kites is generated by all finite-dimensional kites. In particular, we describe some homomorphisms among kites. 相似文献
19.
Yu. M. Movsisyan V. A. Aslanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2013,48(6):241-246
The paper characterizes the class of subdirectly irreducible algebras satisfying hyperidentities of the variety of De Morgan algebras. Such algebras are called subdirectly irreducible De Morgan quasilattices. The suggested characterization is quite close to that of the classical case of subdirectly irreducible DeMorgan algebras. 相似文献
20.
Ján Jakubík 《Mathematica Slovaca》2010,60(2):179-188
The notion of idempotent modification of an algebra was introduced by Je?ek; he proved that the idempotent modification of a group is always subdirectly irreducible. In the present note we show that the idempotent modification of a generalized MV -algebra having more than two elements is directly irreducible if and only if there exists an element in A which fails to be boolean. Some further results on idempotent modifications are also proved. 相似文献