By means of soft intersection-union sum and product, we make a new approach to the hemiring theory via soft set theory with the concepts of soft union (h-ideals, h-bi-ideals, h-quasi-ideals and h-interior ideals). Also, we investigate some characteristics of h-semisimple and h-quasihemiregular hemirings using these kinds of soft union h-ideals. 2000 AMS Classification: 16Y60; 13E05.

Recently new operations have been defined for soft sets. In this paper, we study some important properties associated with these new operations. A collection of all soft sets with respect to new operations give rise to four idempotent monoids. Then with the help of these monoids we can study semiring (hemiring) structures of soft sets. Some of these semirings (hemirings) are actually lattices. ...

Hemirings [3] which provide a common generalization of rings and distributive lattices arise naturally in such diverse areas of mathematics as combinatorics, functional analysis, graph theory, automata theory, mathematical modelling and parallel computation systems etc.(for example, see [3], [4]). Hemirings have also been proved to be an important algebraic tool in theoretical computer science,...