Characterization Of Semialgebras And Its Partial Structures

In this paper, we mainly discuss structures and properties of some semialgebras. In the first section, the concept of semialgebra over semiring is defined. Then, we proved the homomorphic basic theorem, the first and the second isomorphic theorems and discuss the relation between the semialgebras on semiring and the algebras over semiring.In the second section, the ideal, congruence, Idempotent element of semialgebra is raised. Then, we discuss the structures of N - semisimple Artin semialgebras.In the third section, we use the idea of homological algebra to discuss the semialgebras. we generalize the Baer criteria and discuss the division semialgebras and von neumann regular algebras.