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101.
We generalize the concept of an integral residuated lattice to join-semilattices with an upper bound where every principal
order-filter (section) is a residuated semilattice; such a structure is called a sectionally residuated semilattice. Natural examples come from propositional logic. For instance, implication algebras (also known as Tarski algebras), which
are the algebraic models of the implication fragment of the classical logic, are sectionally residuated semilattices such
that every section is even a Boolean algebra. A similar situation rises in case of the Lukasiewicz multiple-valued logic where
sections are bounded commutative BCK-algebras, hence MV-algebras. Likewise, every integral residuated (semi)lattice is sectionally
residuated in a natural way. We show that sectionally residuated semilattices can be axiomatized as algebras (A, r, →, ⇝, 1) of type 〈3, 2, 2, 0〉 where (A, →, ⇝, 1) is a {→, ⇝, 1}-subreduct of an integral residuated lattice. We prove that every sectionally residuated lattice can be isomorphically embedded into a residuated lattice in which the ternary operation r is given by r(x, y, z) = (x · y) ∨ z. Finally, we describe mutual connections between involutive sectionally residuated semilattices and certain biresiduation
algebras.
This work was supported by the Czech Government via the project MSM6198959214. 相似文献
102.
We give a criterion for a linearly ordered topological semilattice to be H-closed. We also prove that any linearly ordered H-closed topological semilattice is absolutely H-closed and we show that every linearly ordered semilattice is a dense subsemilattice of an H-closed topological semilattice. 相似文献
103.
本文研究了左$C$-wrpp半群的加细半格结构,证明了左$C$-wrpp半群是左-${\cal R}$可消带的加细半格当且仅当它是一个$C$-wrpp半群和一个左正则带的织积. 相似文献
104.
We survey tensor products of lattices with zero and related constructions focused on two topics: amenable lattices and box
products.
Received August 21, 1998; accepted in final form September 9, 1998. 相似文献
105.
A new class of semigroups with a two variable regularity law is introduced. These semigroups are non-regular semigroups but they are closely related to regular semigroups. The local and global structures of this class of semigroups are investigated.AMS Subject Classification (2000): 20M10Partially supported by a Chinese University of Hong Kong Direct Research grant, Hong Kong (98/99) # 2060152.Partially supported by a grant of the National Science Foundation, China. 相似文献
106.
S. Yu. Podzorov 《Algebra and Logic》2005,44(2):82-94
We deal in specific features of the algebraic structure of Rogers semilattices of n
0-computable numberings, for n 2. It is proved that any Lachlan semilattice is embeddable (as an ideal) in such every semilattice, and that over an arbitrary non 0-principal element of such a lattice, any Lachlan semilattice is embeddable (as an interval) in it.Supported by INTAS grant No. 00-499, by FP Universities of Russia grant UR.04.01.013, and by the Grant Center for Fundamental Research (GCFR), project PD02-1.1-475.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 148–172, March–April, 2005. 相似文献
107.
We study abstract properties of intervals in the complete lattice of all κ-meet-closed subsets (κ-subsemilattices) of a κ-(meet-)semilattice S, where κ is an arbitrary cardinal number. Any interval of that kind is an extremally detachable closure system (that is, for each closed set A and each point x outside A, deleting x from the closure of A∪{x} leaves a closed set). Such closure systems have many pleasant geometric and lattice-theoretical properties; for example, they are always weakly atomic, lower locally Boolean and lower semimodular, and each member has a decomposition into completely join-irreducible elements. For intervals of κ-subsemilattices, we describe the covering relation, the coatoms, the ∨-irreducible and the ∨-prime elements in terms of the underlying κ-semilattices. Although such intervals may fail to be lower continuous, they are strongly coatomic if and only if every element has an irredundant (and even a least) join-decomposition. We also characterize those intervals which are Boolean, distributive (equivalently: modular), or semimodular.
Mathematics Subject Classifications (2000) Primary: 06A12; Secondary: 06B05, 06A23, 52A01. 相似文献
108.
109.
We describe the semilattice of ordered compactifications of X × Y smaller than o
X × o
Y where X and Y are certain totally ordered topological spaces, and where o
Z denotes the Stone–ech ordered- or Nachbin-compactification of Z. These basic cases are used to illustrate techniques for describing the semilattice of ordered compactifications of X × Y smaller than o
X × o
Y for arbitrary totally ordered topological spaces X and Y. Such products X × Y provide many counterexamples in the theory of ordered compactifications. 相似文献
110.
在序半群上定义了几种新的关系,利用它们得到了序半群上最小完全半素理想的结构,并以此给出了序半群的最小正则半格同余的另一种描述,所得结果是Miroslav Ciric在文[1]中的部分结果向序半群上的推广。 相似文献