Giri and Wazalwar evolved concepts of prime ideal and prime radical in noncommutative semigroups. A hemiring is a ring without subtraction (additive inverse), may not have commutativity and identity. A hemiring with identity is called a semiring. It is well known that a hemiring can be embedded in a semiring. We will use this fact to develop proofs of some results on prime radical in a hemiring...

We extend the notion of intersection of a radical class with the sum of radical classes of rings due to Y. Lee and R. E. Propes (see [3, 4]) to the intersection of a radical class with the sum of radical classes of hemirings. A few results of (see [1, 3, 4]) can be concluded from this paper. AMS Mathematics Subject Classification (2000): 16Y60, 16W50

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.

The present paper indicate a method of obtaining the Hewitt realcompactification vX of a Tychonoff space X, by considering a distinguished family of maximal regular congruences, viz., those which are real, on the hemiring C+(X) of all the non-negative real valued continuous functions on X.

In this paper, the concept of an (∈,∈∨qk)-intuitionistic fuzzy ideal of a hemiring, which is a generalization of the concept of an(∈,∈∨qk)-intuitionistic fuzzy ideal of a hemiring.. Also, we study some of their basic properties. Mathematics subject classification: 08A72 • 03F55 • 20M12