Factorially closed subrings of commutative rings

Chakraborty, Sagnik; Gurjar, Rajendra; Miyanishi, Masayoshi

doi:10.2140/ant.2015.9.1137

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Factorially closed subrings of commutative rings

Sagnik Chakraborty, Rajendra Vasant Gurjar and Masayoshi Miyanishi

Vol. 9 (2015), No. 5, 1137–1158

DOI: 10.2140/ant.2015.9.1137

Abstract

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.

Keywords

factorially closed subring

Mathematical Subject Classification 2010

Primary: 13A05

Secondary: 13B99, 14R05

Milestones

Received: 22 December 2014

Revised: 4 May 2015

Accepted: 9 May 2015

Published: 21 June 2015

Authors

Sagnik Chakraborty
School of Mathematics Tata Institute of Fundamental Research Homi-Bhabha Road, Navy Nagar Mumbai 400005 India

Rajendra Vasant Gurjar
School of Mathematics Tata Institute of Fundamental Research Homi-Bhabha Road, Navy Nagar Mumbai 400005 India

Masayoshi Miyanishi
Research Center for Mathematical Sciences Kwansei Gakuin University 2-1, Gakuen Sanda 669-1337 Japan

Vol. 9, No. 5, 2015