Properties of Standard n-Ideals of a Lattice |
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Authors: | A S A Noor M A Latif |
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Institution: | (1) Department of Mathematics, Rajshahi University, Rajshahi, 6205, Bangladesh |
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Abstract: | An n-ideal of a lattice L is a convex sublattice containing a fixed element n L and it is called standard if it is a standard element of the lattice of n-ideals In(L). In this paper we have shown that, for a neutral element n of a lattice L, the principal n-ideal a n of a lattice L is a standard n-ideal if and only if a n is standard and a n is dual standard. We have also shown that if n is a neutral element and (n] and n) are relatively complemented, then every homomorphism n-kernels of L is a standard n-ideal and every standard n-ideal is the n-kernel of precisely one congruence relation. Finally, we have shown that, for a relatively complemented lattice L with 0 and 1, C(L) is a Boolean algebra if and only if every standard n-ideal of L is a principal n-ideal.AMS Subject Classification (2000) 06B10 06B99 06C15 |
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Keywords: | convex sublattice standard n-ideal neutral element homomorphism n-kernel boolean algebra |
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