Some Studies Of Semimodules About Lizuka-congruence

In the paper,We mainly investigate the properties semimmodules about Iizuka-congruence and application,Investigate the quotient semimmodules properties and Three basic isomorphism theorem about Iizuka-congruence;The semimmodules about Iizuka-congruence with remaining short pseudo column was the basic properties and applications.This study includes four chapters.The first chapter is Preliminaries,First introduced some research background and development situation about this paper;And then mainly introduces related definition and conclusion this article needed.In the second section is introduction concept about Iizuka-congruence on semimmodules,Given with the rest basic properties of the semimmodules in Iizuka-congruence,And according to the basic isomorphism theorem of the semimmodulesdomain,Let’s get some properties of quotient semimmodules about Iizuka-congruence.In the third section,on the basis of the exact columns of the semimmodules,To study the semimmodules sequence in extension about Iizuka-congruence,introduced the concept of short pseudo column,And discussed its related properties,such as:Short pseudo exact sequence’s pseudo exactness and pseudo exact sequence’s basic Properties.The last section,according to what they have learned before Some common theorem about Sequence of the semimmodules,such as: five lemma,three lemma,cleavability.Use Chapter three relevant properties and theorems Is derived Short pseudo exact sequence some important applications.