MMN-2201
On the structure of balanced near semirings
Ivan Chajda; Helmut Langer;Abstract
The concept of a balanced near semiring was introduced by the authors in their paper entitled "Near semirings and semirings with involution" (which is to appear in Miskolc Math. Notes) in order to describe ring-like structures derived by means of lattices with involution, in particular with complementation. Now we show that every such balanced near semiring has an underlying structure which is a Boolean algebra. Based on this result, we describe ideals of these near semirings. A natural one-to-one correspondence between ideals and congruences is established.
Vol. 18 (2017), No. 2, pp. 691-699