Principally Quasi injective system over monoid

Abstract

In this work , principally quasi injective system has been introduced and studied , which is a generalization of quasi injective system . We obtain a characterizations of  PQ-injective systems , conditions on which, subsystems inherit  the property of PQ-injectivity , and conditions have been considered to versus PQ-injective system. Finally , the relationship between maximal reversible subsystem of system  and maximal left ideal of the endomorphism monoid of the system has been studied  .