Octahedron Subgroups and Subrings

Jeong-Gon Lee, Young Bae Jun and Kul Hur
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Jeong-Gon Lee: Division of Applied Mathematics, Wonkwang University, 460, Iksan-daero, Iksan-Si, Jeonbuk 54538, Korea
Young Bae Jun: Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
Kul Hur: Division of Applied Mathematics, Wonkwang University, 460, Iksan-daero, Iksan-Si, Jeonbuk 54538, Korea

Mathematics, 2020, vol. 8, issue 9, 1-32

Abstract: In this paper, we define the notions of i -octahedron groupoid and i -OLI [resp., i -ORI and i -OI], and study some of their properties and give some examples. Also we deal with some properties for the image and the preimage of i -octahedron groupoids [resp., i -OLI, i -ORI and i -OI] under a groupoid homomorphism. Next, we introduce the concepts of i -octahedron subgroup and normal subgroup of a group and investigate some of their properties. In particular, we obtain a characterization of an i -octahedron subgroup of a group. Finally, we define an i -octahedron subring [resp., i -OLI, i -ORI and i -OI] of a ring and find some of their properties. In particular, we obtain two characterizations of i -OLI [resp., i -ORI and i -OI] of a ring and a skew field, respectively.

Keywords: octahedron set; i -octahedron subgroupoid; i -octahedron ideal; i -sup-property, i -octahedron subgroup; i -octahedron subring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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