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In this paper we continue the study of various ring theoretic properties of Morita contexts. Necessary and sufficient conditions are obtained for a general Morita context or a trivial Morita context or a formal triangular matrix ring to satisfy a certain ring property which is among being Kasch, completely primary, quasi-duo, 2-primal, NI, semiprimitive, projective-free, etc. We also characterize when a general Morita context is weakly principally quasi-Baer or strongly right mininjective. [ABSTRACT FROM AUTHOR]

A ring R is called a left P S -ring if its left socle, Soc (R R) , is projective. Equivalently, R is left P S -ring if the right annihilator of every maximal left ideal is of the form e R , where e is an idempotent in R. In this paper, we characterize when a (trivial) Morita context or a generalized triangular matrix ring is a left P S -ring. Examples to illustrate and delimit the theory are provided. [ABSTRACT FROM AUTHOR]