On the representation of distributive semilattices

1994 ◽  
Vol 31 (3) ◽  
pp. 446-455 ◽  
Author(s):  
Michael Tischendorf
Keyword(s):  
Distributive Semilattices

scholarly journals O-Distributive Semilattices

1978 ◽  
Vol 21 (4) ◽  
pp. 469-475 ◽  
Author(s):  
Y. S. Pawar ◽  
And N. K. Thakare
Keyword(s):  
Sufficient Conditions ◽  
Distributive Semilattices

AbstractSufficient conditions for a semilattice to be a 0- distributive are obtained. Some equivalent formulations of 0- distributivity in a semilattice are given. Further, disjunctive 0- distributive semilattices are also characterized.

scholarly journals Monotonic Distributive Semilattices

Order ◽  
2018 ◽  
Vol 36 (3) ◽  
pp. 463-486
Author(s):  
Sergio A. Celani ◽  
Ma. Paula Menchón
Keyword(s):  
Distributive Semilattices

Notes on mildly distributive semilattices

2017 ◽  
Vol 67 (5) ◽  
Author(s):  
Sergio Arturo Celani ◽  
Luciano Javier González
Keyword(s):  
Prime Ideals ◽  
Distributive Semilattice ◽  
Definition Of ◽  
Distributive Semilattices ◽  
Distributive Extension

AbstractIn this paper we shall investigate the mildly distributive meet-semilattices by means of the study of their filters and Frink-ideals as well as applying the theory of annihilator. We recall some characterizations of the condition of mildly-distributivity and we give several new characterizations. We prove that the definition of strong free distributive extension, introduced by Hickman in 1984, can be simplified and we show a correspondence between (prime) Frink-ideals of a mildly distributive semilattice and (prime) ideals of its strong free distributive extension.

scholarly journals Non-representable distributive semilattices

2008 ◽  
Vol 212 (11) ◽  
pp. 2503-2512 ◽  
Author(s):  
Miroslav Ploščica
Keyword(s):  
Distributive Semilattices

The word problem in the tensor product of distributive semilattices

1984 ◽  
Vol 30 (1) ◽  
pp. 117-120 ◽  
Author(s):  
Grant A. Fraser ◽  
Andrew M. Bell
Keyword(s):  
Tensor Product ◽  
Word Problem ◽  
Distributive Semilattices

scholarly journals Mildly distributive semilattices

1984 ◽  
Vol 36 (3) ◽  
pp. 287-315 ◽  
Author(s):  
Robert Hickman
Keyword(s):  
Congruence Distributive ◽  
Distributive Semilattices

AbstractThere is no single generalization of distributivity to semilattices. This paper investigates the class of mildly distributive semilattices, which lies between the two most commonly discussed classes in this area—weakly distributive semilattices and distributive semilattices. Particular attention is paid to describing and characterizing congruence distributive mildly distributive semilattices, in contrast to distributive semilattices, whose lattice of join partial congruences is badly behaved and which are difficult to describe.

Local separation in distributive semilattices

2005 ◽  
Vol 54 (3) ◽  
pp. 323-335 ◽  
Author(s):  
Miroslav Ploščica
Keyword(s):  
Distributive Semilattices

scholarly journals Some remarks on certain classes of semilattices

1982 ◽  
Vol 5 (1) ◽  
pp. 21-30 ◽  
Author(s):  
P. V. Ramana Murty ◽  
M. Krishna Murty
Keyword(s):  
Necessary And Sufficient Condition ◽  
Dense Element ◽  
Pseudocomplemented Semilattice ◽  
Distributive Semilattice ◽  
Interesting Corollary ◽  
Definition Of ◽  
Almost All ◽  
Necessary And Sufficient ◽  
Distributive Semilattices ◽  
Natural Way

In this paper the concept of a∗-semilattice is introduced as a generalization to distributive∗-lattice first introduced by Speed [1]. It is shown that almost all the results of Speed can be extended to a more eneral class of distributive∗-semilattices. In pseudocomplemented semilattices and distributive semilattices the set of annihilators of an element is an ideal in the sense of Grätzer [2]. But it is not so in general and thus we are led to the definition of a weakly distributive semilattice. In§2we actually obtain the interesting corollary that a modular∗-semilattice is weakly distributive if and only if its dense filter is neutral. In§3the concept of a sectionally pseudocomplemented semilattice is introduced in a natural way. It is proved that given a sectionally pseudocomplemented semilattice there is a smallest quotient of it which is a sectionally Boolean algebra. Further as a corollary to one of the theorems it is obtained that a sectionally pseudocomplemented semilattice with a dense element becomes a∗-semilattice. Finally a necessary and sufficient condition for a∗-semilattice to be a pseudocomplemented semilattice is obtained.

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