Factorization properties of quotients of polynomial and power series rings by monomial ideals

Abstract

Suppose that K is a field, $S=K[x_1,\dots ,x_n]$ or $S=K[[x_1,\dots ,x_n]]$ and I is a monomial ideal of S. We study factorization properties of the ring $R=S/I$. In particular, we present conditions equivalent to R being présimplifiable, a bounded factorization ring, a finite factorization ring or a unique factorization ring.

KEYWORDS:

• Bounded factorization ring
• finite factorization ring
• monomial ideal
• polynomial ring
• power series ring
• unique factorization ring

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13F15
• 13A05
• 13F55

Acknowledgments

The authors would like to thank the referee for his/her careful reading of the paper and nice comments.