**Semiring Theory**

**Semirings are ring-like algebraic structures where subtraction is either impossible or disallowed. They are interesting generalizations of rings and distributive lattices and have important applications in many branches of science and engineering.**

**A course on semiring theory may include the following topics:**

**Definition of semirings and examples****Building new semirings from old examples****Distinguished elements of semirings (zero-divisors, nilpotents, idempotents, units, complemented elements, and so on)****Ideal theory in semirings (prime, semiprime, primary, and maximal ideals)****Factor semirings****Morphisms of semirings and their kernels****Semirings of fractions (quotient theory): Bourne, Iizuka, and partitioning****Semimodules over semirings****Factor semimodules**

**An advanced course on semirings may include the following additional topics:**

**Linear algebra over semirings****Partially-ordered semirings****Complete semirings****Complete semimodules**

For more on semiring theory refer to the following book:

Golan, J. S. (2013). Semirings and their Applications. Springer Science & Business Media.

**Other courses on algebra:**

For a brief history of algebra, see the following page: