半环类■°I中成员的性质和结构

The property and structure of members of the class ■°I of semirings

利用半环上的同余关系,研究了半环类.■°I中成员的性质.分别研究了半环类.O∩■°■B和■∩■°■中成员的次直积分解,并利用"(2,2)型代数的坚固构架"的概念,证明了半环S∈■°■l是■与■l中成员的次直积当且仅当S的乘法半群是群与半格的次直积.

By using the congruences on a semiring, the properties of members of the class G°I of semirings are obtained. The subdirect product decompositions of the members of the classes O∩G°NB and O∩G°R of semirings are studied, respectively. And it is proved that a serniring S in G°Sl is a subdirect product of a member of G and a member of Sl if and only if the multiplicative reduct of S is a subdirect product of a group and a semilattice by using the concept of sturdy frame of type （2,2） algebras.