Quasi ideals of nearness semirings

Abstract

This article introduces quasi-ideals in semirings on weak nearness approximation spaces. Concepts and definitions are given to clarify the subject of quasi ideals in semirings on weak nearness approximation spaces. Some basic properties of quasi ideals are also given. Furthermore, it is given that the definition of upper-near quasi ideals. And, it is examined that the relationship between quasi ideals and upper near quasi ideals. Therefore, the features described in this study will contribute greatly to the theoretical development of the nearness semirings theory.

Quotient Nearness d-Algebras

“…In 2012, İnan and Öztürk analyzed the concept of nearness groups and investigated their basic properties ( [2]). After, in [3] and [13] the nearness semigroups and nearness rings were established and their basic properties were investigated respectively (and other algebraic approaches of near sets in see [10], [12], [14], [15], [16], [16], [19], [27], [28], and [29]).…”