Pseudo C-M-Injective and Pseudo C-Quasi Principally Injective Systems Over Monoids
Abstract
In this paper, the concepts of pseudo C-quasi injective and pseudo C-quasi principally injective systems over monoids are introduced which represents generalizations of quasi injective and quasi principally injective respectively. Characterization of these concepts are given . At the same time some properties of pseudo C-quasi principally injective systems are studied in terms of their endomorphism monoid. Relate the conceptsof Hopfian , co-Hopfianand directly finite with pseudo C-quasi injective systems over monoids. Conditions are investigated under which subsystems are inheritpseudo C-quasi principally injective and pseudo C-quasi injective. The relationship among the class of pseudo C-quasi injective and pseudo C-quasi principally injective systems with some generalizations of injectivity (such as extending and continuous systems ) are considered .
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