Amitsur's theorem, semicentral idempotents, and additively idempotent semirings

Abstract

The article explores research findings akin to Amitsur’s theorem, asserting that any derivation within a matrix ring can be expressed as the sum of an inner derivation and a hereditary derivation. In most results related to rings and semirings, Birkenmeier’s semicentral idempotents play a crucial role. This article is intended for PhD students, postdocs, and researchers.

Keywords

• differential algebra
• derivations
• matrices
• matrix rings
• endomorphisms
• endomorphism rings
• idempotents
• semicentral idempotents
• additive basis
• skew ore polynomials
• additively idempotent semirings
• matrix semirings
• polynomial semirings
• endomorphism semirings
• 12h05
• 13n15
• 15a30
• 15a80
• 15b33
• 16s32
• 16s50
• 16u40
• 16w20
• 16w25
• 16y60