Convex L-lattice subgroups in L-ordered groups

Publish Year: 1397
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:

JR_CGASAT-9-1_006

تاریخ نمایه سازی: 23 شهریور 1400

Abstract:

In this paper, we have focused to study convex L-subgroups of an L-ordered group. First, we introduce the concept of a convex L-subgroup and a convex L-lattice subgroup of an L-ordered group and give some examples. Then we find some properties and use them to construct convex L-subgroup generated by a subset S of an L-ordered group G . Also, we generalize a well known result about the set of all convex subgroups of a lattice ordered group and prove that C(G), the set of all convex L-lattice subgroups of an L-ordered group G, is an L-complete lattice on height one. Then we use these objects to construct the quotient L-ordered groups and state some related results.

Keywords:

L-ordered group , convex L-subgroup , (normal) convex L-lattice subgroup

Authors

Rajabali Borzooei

Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran.

Fateme Hosseini

Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran.

Omid Zahiri

University of Applied Science and Technology, Tehran, Iran

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