Corrigendum to “New algebraic properties of an amalgamated algebra along an ideal”

ABSTRACT

At some point, after publication, we realized that Proposition 4.1(2) and Theorem 4.4 in [2] hold under the assumption (not explicitly declared) that B = f(A)+J. Furthermore, we provide here the exact value for the embedding dimension of A⋈^fJ, also when B≠f(A)+J, under the hypothesis that J is finitely generated as an ideal of the ring f(A)+J.

KEYWORDS:

• Cohen-Macaulay
• D+M construction
• embedding dimension
• Gorenstein
• idealization
• Krull dimension
• pullback
• Zariski topology

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 13A15
• 13B99
• 14A05

Acknowledgment

This work was partially supported by GNSAGA of Istituto Nazionale di Alta Matematica. The second author was also supported by a Post Doc Grant from the University of Technology of Graz - Austrian Science Fund (FWF), # P 27816.