Algebra & Number Theory
- Algebra Number Theory
- Volume 9, Number 5 (2015), 1137-1158.
Factorially closed subrings of commutative rings
We prove some new results about factorially closed subrings of commutative rings. We generalize this notion to quasifactorially closed subrings of commutative rings and prove some results about them from algebraic and geometric viewpoints. We show that quasifactorially closed subrings of polynomial and power series rings of dimension at most three are again polynomial (resp. power series) rings in a smaller number of variables. As an application of our results, we give a short proof of a result of Lê Dũng Tráng in connection with the Jacobian problem.
Algebra Number Theory, Volume 9, Number 5 (2015), 1137-1158.
Received: 22 December 2014
Revised: 4 May 2015
Accepted: 9 May 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
factorially closed subring
Chakraborty, Sagnik; Gurjar, Rajendra; Miyanishi, Masayoshi. Factorially closed subrings of commutative rings. Algebra Number Theory 9 (2015), no. 5, 1137--1158. doi:10.2140/ant.2015.9.1137. https://projecteuclid.org/euclid.ant/1510842358