Right (left) nearregular seminearrings

Document Type : Original Paper

Authors

1 Department of mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

Abstract

In this paper, as a generalization of regular and strongly regular elements of a semi near rings, we introduce the Concept of ( left ) right near regular elements. In the following, we investigate some properties of near regular semi near rings and presents the connection between reduced and strongly reduced elements.

Keywords

Main Subjects


[1] Cho Y. U. and Hirano Y., Strong reducedness and strong regularity for near-rings, Kyungpook Math.
J, 43 (2003) 587-592.
[2] Ferrero G., Nearrings: some developments linked to semigroups and groups, Springer Science and
Business Media (2013).
[3] Golan J. S., Semirings and their Applications, Springer Science and Business Media (2013).
[4] Goodearl K. R., Von Neumann regular rings, London, Pitman (1979).
[5] Mason G., Strongly regular near-rings, Proceedings of the Edinburgh Mathematical Society, 231
(1980) 27-35.
[6] Pilz G., Near-rings, the theory and its applications, Elsevier (2011).
[7] Reddy Y. V. and Murty C. V. L. N., On strongly regular near-rings, Proceedings of the Edinburgh
Mathematical Society, 271 (1984) 61-64.
[8] Sardar S. K. and Mukherjee R., On additively regular seminearrings, In Semigroup Forum, Springer
US, 883 (2014) 541-554.
[9] Satyanarayana B. and Prasad K. S., Near rings, fuzzy ideals, and graph theory, Chapman and
Hall/CRC. (2013).