On semisimple semirings

Abstract

We investigate ideal-semisimple and congruence-semisimple semirings. We give several new characterizations of such semirings using e-projective and e-injective semimodules. We extend several characterizations of semisimple rings to (not necessarily subtractive) commutative semirings.

Keywords:

• Injective semimodules
• projective semimodules
• semimodules
• semirings
• semisimple semirings

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 16D60
• Secondary 16D40
• 16D50

Additional information

Funding

The authors would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through projects nos. RG1304-1 & RG1304-2.