Prime and implicative semilattices

1980 ◽  
Vol 10 (1) ◽  
pp. 31-35
Author(s):  
P. V. Ramana Murty
Keyword(s):  
Implicative Semilattices

Pseudocomplemented and Implicative Semilattices

1982 ◽  
Vol 34 (2) ◽  
pp. 423-437 ◽  
Author(s):  
C. S. Hoo
Keyword(s):  
Boolean Algebra ◽  
Closed Algebra ◽  
Implicative Semilattices

Let L be a semilattice and let a ∊ L. We refer the reader to Definitions 2.2, 2.4, 2.5 and 2.12 below for the terminology. If L is a-implicative, let Ca be the set of a-closed elements of L, and let Da be the filter of a-dense elements of L. Then Ca is a Boolean algebra. If a = 0, then C0 and D0 are the usual closed algebra and dense filter of L. If L is a-admissible and f : Ca × Da → Da is the corresponding admissible map, we can form a quotient semilattice Ca × D0f. In case a = 0, Murty and Rao [4] have shown that C0 × D0/f is isomorphic to L, and hence that C0 × D0 is 0-admissible. In case L is in fact implicative, Nemitz [5] has shown that C0 × D0/f is isomorphic to L, and that C0 × D0/f is also implicative.

scholarly journals Relative annihilators in semilattices

1973 ◽  
Vol 9 (2) ◽  
pp. 169-185 ◽  
Author(s):  
J.C. Varlet
Keyword(s):  
Lower Bound ◽  
Principal Ideal ◽  
The Other ◽  
Fixed Element ◽  
Other Hand ◽  
The One ◽  
Implicative Semilattices

An α-distributive (respectively α-implicative) semilattice S is a lower semilattice (with greatest lower bound denoted by juxtaposition) in which the annihilator 〈x, a〉, that is {y ∈ S: xy ≤ α}, is an ideal (respectively a principal ideal) for the fixed element α and any x of S. These semilattices appear as natural links between general and distributive semi-lattices on the one hand, and between pseudo-complemented and implicative semilattices on the other hand. Prime and dense elements, as well as maximal and prime filters, are essential. Mandelker's result, a lattice L is distributive if and only if 〈x, y〉 is an ideal for any x, y ∈ L is extended to semi-lattices.

scholarly journals Varieties of implicative semilattices

1971 ◽  
Vol 37 (3) ◽  
pp. 759-769 ◽  
Author(s):  
William Nemitz ◽  
Thomas Whaley
Keyword(s):  
Implicative Semilattices

On filters of implicative semilattices

2002 ◽  
Vol 143 (1-4) ◽  
pp. 197-204
Author(s):  
Young Bae Jun
Keyword(s):  
Implicative Semilattices

Irreducibility in implicative semilattices

1979 ◽  
Vol 9 (1) ◽  
pp. 244-249
Author(s):  
William C. Nemitz
Keyword(s):  
Implicative Semilattices

Esakia Style Duality for Implicative Semilattices

2011 ◽  
Vol 21 (2) ◽  
pp. 181-208 ◽  
Author(s):  
Guram Bezhanishvili ◽  
Ramon Jansana
Keyword(s):  
Implicative Semilattices

scholarly journals Identities in implicative semilattices

1973 ◽  
Vol 41 (2) ◽  
pp. 443-443
Author(s):  
Angelo Margaris
Keyword(s):  
Implicative Semilattices

l-Hemi-Implicative Semilattices

Studia Logica ◽  
2017 ◽  
Vol 106 (4) ◽  
pp. 675-690 ◽  
Author(s):  
José Luis Castiglioni ◽  
Hernán Javier San Martín
Keyword(s):  
Implicative Semilattices
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