On the almost Gorenstein property of determinantal rings

ABSTRACT

In this paper, we investigate the question of when the determinantal ring R over a field k is an almost Gorenstein local/graded ring in the sense of [14]. As a consequence of the main result, we see that if R is a non-Gorenstein almost Gorenstein local/graded ring, then the ring R has a minimal multiplicity.

KEYWORDS:

• Almost Gorenstein graded ring
• almost Gorenstein local ring
• determinantal ring

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 13H10
• 13H15
• 13A02

Acknowledgements

The author would like to thank Kazuhiko Kurano and Mitsuyasu Hashimoto for their valuable advices and comments.

The author was partially supported by JSPS Grant-in-Aid for Young Scientists (B) 17K14176