Cohen–Macaulay and Gorenstein Properties under the Amalgamated Construction

Abstract

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 ⋈^fJ: = {(a, f(a) + j)|a ∈ A and j ∈ J} of A × 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 ⋈^fJ.

Key Words:

• Amalgamated algebra
• Cohen–Macaulay ring
• Gorenstein ring
• Quasi-Gorenstein ring
• Serre condition
• Universally catenary ring

2010 Mathematics Subject Classification:

• Primary: 13A15
• 13H10
• 13C15

ACKNOWLEDGMENT

The authors are deeply grateful to the referee for his/her careful reading of the article and valuable suggestions.