Characterization of the complete homomorphic images of a completely distributive complete lattice. II
نویسندگان
چکیده
منابع مشابه
HOMOMORPHIC IMAGES OF a-COMPLETE BOOLEAN ALGEBRAS
It is a well-known theorem of R. S. Pierce that, for every infinite cardinal a, a 0 = a if and only if there is a complete Boolean algebra B s.t. card B = a (see [3, Theorem 25.4]). Recently, Comfort and Hager proved [l] that, for every infinite a-complete Boolean algebra B, (card B) 0 _ card B. We extend this result to the class of homomorphic images of cr-complete algebras, following closely ...
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4. Proof of Theorem 2. Harish-Chandra [l] and others have proved that every Lie algebra over a field of characteristic zero has a faithful representation. Consequently by Lemma 4, 8 has a faithful representation x—*Qx whose matrices have elements in an algebraic extension $ of g such that t(QxQv) =0 for all x of 31 and all y of 8. We now apply another form of Cartan's criterion for solvability ...
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It is well known that the only simple distributive lattice is the twoelement chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences. In this paper we show the existence of infinite complete-simple distributive lattices. “COMPLETE-SIMPLE” DISTRIBUTIVE LATTICES G. GRÄTZER A...
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In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...
متن کاملTotal graph of a $0$-distributive lattice
Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, and ${rm Z}(£)$ its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by ${rm T}(G (£))$. It is the graph with all elements of £ as vertices, and for distinct $x, y in £$, the vertices $x$ and $y$ are adjacent if and only if $x vee y in {rm Z}(£)$. The basic properties of the ...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1983
ISSN: 1385-7258
DOI: 10.1016/1385-7258(83)90040-9