The Journal of the Indian Mathematical Society

Iqbalunnisa

Abstract

This paper deals with neutral elements and shows that it is possible to define neutrality of an element by a single equality, (i.e., a solution to problem 3 of [3] ). It also extends the theorem of J . Von Neumann that "an element of a complemented modular lattice L is neutral if and only if its complement is unique" to relatively complemented lattices, (i.e., solution to problem 16 of [3] ).

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Iqbalunnisa ¹

Affiliations
1 Madras University, Madras-5, IN

Abstract

This paper characterizes the congruence classes under a congruence θ on a lattice L, and gives a solution to Problem 72 of Lattice Theory by G. Birkhoff, revised edition (1948).

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