Semirings
Abstract
We survey theory developed over the past 10 years of semirings which need not be additively cancellative. The main features are a specified ``null ideal'' $\mcA_0$ of a semiring $\mcA,$ taking the place of a zero element, and a ``surpassing relation,'' taking the place of equality, which permit generalizations of the classical algebraic theory to polynomials and their roots, algebraic geometry, matrices, linear algebra, varieties, categories, and module theory. The ``pair'' $(\mcA,\mcA_0)$ is studied along the lines of universal algebra.
Fields of Study & Subjects
Rings
Modules
and Algebras
semigroups and automata theory
Advanced Algebra and Logic
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 22 February 2026
- Language
- EN
- Document type
- Preprint