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Representation of certain classes of distributive lattices by sections of sheaves
International Journal of Mathematics and Mathematical Sciences, Volume 3, Issue 3, Page 461-476, 1980., 1979 Epstein and Horn ([6]) proved that a Post algebra is always a P‐algebra and in a P‐algebra, prime ideals lie in disjoint maximal chains. In this paper it is shown that a P‐algebra L is a Post algebra of order n ≥ 2, if the prime ideals of L lie in disjoint maximal chains each with n − 1 elements.
U. Maddana Swamy, P. Manikyamba
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A Sheaf Representation of Distributive Pseudocomplemented Lattices [PDF]
Proceedings of the American Mathematical Society, 1976 The main result of this paper shows that a distributive pseudocomplemented lattice ( L ; ∨
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Sectionally Pseudocomplemented Residual Lattice
Daffodil International University Journal of Science and Technology, 1970 At first, we recall the basic concept, By a residual lattice is meant an algebra L = (L,∨,∧,∗,o,0,1) such that (i) L = (L,∨,∧,0,1) is a bounded lattice, (ii) L = (L,∗,1) is a commutative monoid, (iii) it satisfies the so-called adjoin ness property: (x ∨ y) ∗ z = y if and only if y ≤ z ≤ x o y Let us note [7] that x ∨ y is the greatest element of the ...
Rahman, Md. Zaidur +2 more
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Congruences on distributive pseudocomplemented lattices [PDF]
Bulletin of the Australian Mathematical Society, 1973 Let B0 ⊂ B1 ⊂ Bn ⊂ … ⊂: Bw be all the non-trivial varieties of distributive pseudocomplemented lattices (L; ∨, ∧, *, 0, 1) considered as algebras of type (2, 2, 1, 0, 0). A subset J of such an algebra L is a congruence-kernel if and only if it is a lattice-ideal and x** ∈ J for each x ∈ J. The smallest congruence having J as its kernel is Θ(J), where a
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Finitely generated pseudocomplemented distributive lattices [PDF]
Journal of the Australian Mathematical Society, 1975 If L is a pseudocomplemented distributive lattice which is generated by a finite set X, then we will show that there exists a subset G of L which is associated with X in a natural way that ¦G¦ ≦ ¦X¦ + 2¦x¦ and whose structure as a partially ordered set characterizes the structure of L to a great extent.
Berman, J., Dwinger, Ph.
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Nontrivially pseudocomplemented lattices are complemented [PDF]
Proceedings of the American Mathematical Society, 1979 Nontrivially pseudocomplemented lattices are complemented.
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Principal congruences of pseudocomplemented distributive lattices [PDF]
Proceedings of the American Mathematical Society, 1973 Principal congruences of pseudocomplemented distributive lattices are characterized. This characterization is used to give a new proof of the congruence extension property and to show that the meet of two principal congruences is always principal in an equational class of pseudocomplemented distributive lattices if and only if the class is a subclass ...
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Implications in pseudocomplemented and Stone lattices
Two kinds of the connective implication are introduced as term operations of a pseudocomplemented lattice. It is shown that they share a lot of properties with the intuitionistic implication based on Heyting algebras. In particular, if the pseudocomplemented lattice in question is a Stone lattice then the considered implications satisfy some kind of ...
Chajda, Ivan, Länger, Helmut
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Pseudocomplemented distributive lattices with small endomorphism monoids [PDF]
Bulletin of the Australian Mathematical Society, 1983 By a result of K.B. Lee, the lattice of varieties of pseudo-complemented distributive lattices is the ω + 1 chainwhere B−1, B0, B1 are the varieties formed by all trivial, Boolean, and Stone algebras, respectively. General theorems on relative universality proved in the present paper imply that there is a proper class of non-isomorphic algebras in B3 ...
Adams, M. E., Koubek, V., Sichler, J.
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EXTERNALLY COMPATIBLE IDENTITIES IN PSEUDOCOMPLEMENTED DISTRIBUTIVE LATTICES
Demonstratio Mathematica, 1987 exaly +2 more sources