An analysis of hereditary and pure hereditary ring using a triangular matrix ring

Abstract

In this paper the hereditary ring is considered, defined, classified and studied which is associative with unit where an ideal of R is T. Considering the ring B=B′/J is regular ring (where let B′ as a regular ring that is commutative but not semi-simple and J be the ideal of ). B′ First of all, R has shown as a left Hereditary and Noetherian Hereditary ring. A triangular matrix ring has been taken which is shown as left hereditary forming with two left Hereditary Ring R and S. Finally we have declared that although the ring R is not a right semi-Hereditary but must be left hereditary [2]. Accordingly, we can say that R is not a right pure-Hereditary ring.