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arXiv · 1403.1542

$L$-Ordered and $L$-Lattice Ordered Groups

R. A. Borzooei·A. Dvurečenskij·O. Zahiri
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Abstract

This paper pursues an investigation on groups equipped with an $L$-ordered relation, where $L$ is a fixed complete complete Heyting algebra. First, by the concept of join and meet on an $L$-ordered set, the notion of an $L$-lattice is introduced and some related results are obtained. Then we applied them to define an $L$-lattice ordered group. We also introduce convex $L$-subgroups to construct a quotient $L$-ordered group. At last, a relation between the positive cone of an $L$-ordered group and special type of elements of $L^G$ is found, where $G$ is a group.

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R. A. Borzooei, A. Dvurečenskij, O. Zahiri. 2014-03-06. $L$-Ordered and $L$-Lattice Ordered Groups. https://arxiv.org/abs/1403.1542

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