IRREDUCIBLE ELEMENTS IN ALGEBRAIC LATTICES

Autor:	B. Venkateswarlu, U. M. Swamy
Rok vydání:	2010
Předmět:	Combinatorics Algebraic cycle High Energy Physics::Lattice General Mathematics Lattice (order) Integer lattice Dimension of an algebraic variety Irreducible element Mathematics::Representation Theory Congruence lattice problem Map of lattices Irreducible component Mathematics
Zdroj:	International Journal of Algebra and Computation. 20:969-975
ISSN:	1793-6500 0218-1967
DOI:	10.1142/s0218196710005984
Popis:	α-Irreducible and α-Strongly Irreducible Ideals of a ring have been characterized in [2] and [4]. A complete lattice which is generated by compact elements is called an algebraic lattice for the simple reason that every such lattice is isomorphic to the lattice of subalgebras of a suitable universal algebra and vice-versa. In this paper, we characterize the irreducible elements and strongly irreducible elements in an algebraic lattice, which extends the results in [4] to arbitrary algebraic lattices. Also we obtain certain necessary and sufficient conditions, in terms of irreducible elements, for an algebraic lattice to satisfy the complete distributivity.
Databáze:	OpenAIRE
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