Algebra & Number Theory

Factorially closed subrings of commutative rings

Sagnik Chakraborty, Rajendra Gurjar, and Masayoshi Miyanishi

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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.

Article information

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13A05: Divisibility; factorizations [See also 13F15]
Secondary: 13B99: None of the above, but in this section 14R05: Classification of affine varieties

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.

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