MMN-1936
Near semirings and semirings with involution
Ivan Chajda; Helmut Länger;Abstract
We study so-called near semirings endowed with an antitone involution. Such a near semiring is in fact a bounded lattice which has one more binary operation, the multiplication. We classify several families of bounded lattices which can be organized in such near semirings, e.g. chains or orthomodular lattices. A particular case are the so-called balanced near semirings which form a variety which is congruence distributive, permutable and regular.
Vol. 17 (2016), No. 2, pp. 801-810
DOI: 10.18514/MMN.2017.1936