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In this paper we first introduce the notion of McCoy over prime radicals (MPR ring) which is a generalization of Armendariz over prime radicals (APR ring) and McCoy rings. Then we investigate their properties. For a ring R, we prove that the n-by-n upper triangular matrix ring Tn(R) is MPR. The structure and some of extensions of MPR rings will be further studied and investigated. [ABSTRACT FROM AUTHOR]

Let R be a ring, (S,≤) a strictly ordered monoid and Λ = R[[S,w]] the skew generalized power series ring. In this paper, we investigate the transfer of some ring properties on skew generalized power series rings such as central Armendariz, left fusible, right IN and right SA-rings. In particular we study the conditions under which: (i) R is central(S,w)-Armendariz if R/I is central (S,w)-Armendariz; (ii) V is a left fusible ring; (iii) R is a right IN-ring if V is a right IN-ring; (iv) R is a right SA-ring if V is a right SA-ring. [ABSTRACT FROM AUTHOR]