On Utumi’s quotients and extended centroid of weakly right cancellative semirings

Abstract

In this article, we expand the concept of Utumi’s ring of quotients in the canvas of weakly right cancellative (WRC) semirings. The remarkable result of Martindale et al [4] stated; any derivation d of a semiprime ring R can be extended uniquely to a derivation to ring of quotient, is generalized for WRC semirings. Moreover, we introduce the concept of extended centroid to this certain semirings and discuss some of its salient characteristics.

Subject Classification:

• 16N60
• 16W25
• 16Y60

Keywords:

• Weakly cancellative semirings
• Derivations
• Utumi’s quotients
• Extended centroid