COHEN-MACAULAY AND GORENSTEIN PROPERTIES UNDER THE AMALGAMATED CONSTRUCTION

Let A and B be commutative rings with unity, f : A -> B a ring homomorphism, and J an ideal of B. Then the subring A (sic)(f) J := {(a, f(a) + j)vertical bar a is an element of A and j is an element of J} of A x B is called the amalgamation of A with B along J with respect to f. In this article, among other things, we investigate the Cohen-Macaulay and (quasi-) Gorenstein properties on the ring A (sic)(f) J.