Article

Division closed lattice-ordered rings and commutative L*-rings

Published in: Quaestiones Mathematicae
Volume 42 , issue 8 , 2019 , pages: 1019–1029

DOI: 10.2989/16073606.2018.1503201

Author(s): Jingjing Ma Department of Mathematics and Statistics, USA , Jessica Smith Department of Mathematics and Statistics, USA

Keywords: Primary 06F25 , Primary 06F25

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Abstract

The paper continues the study of division closed lattice-ordered rings and commutative L*-rings. More interesting properties of division closed lattice-ordered rings are presented and it is shown that under certain conditions such rings are f-rings. The main result on L*-rings is that for a commutative semilocal ring with the identity, it is L* if and only if it is O*.

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