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All Journal Jurnal Matematika UNAND
Yassin Dwi Cahyo
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Computer Science & IT Mathematics

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SOME PROPERTIES OF CLEAR RINGS Yassin Dwi Cahyo; PERMATASARI, C. NOVITA; SUBASTIAN, NANDA; FARIZI, SALMAN; PUSPITA, NIKKEN PRIMA; SURYOTO, SURYOTO
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.196-212.2026

Abstract

Let (R, +, ยท) be a ring with unity. An element in R is called a cleanelement if it is the sum of a unit element and an idempotent element. A ring R is calleda clean ring if all elements in R are clean elements. The notion of a clean element wasgeneralized to a clear element by replacing the idempotent element with a unit-regularelement. An element in R is called a clear element if it is the sum of a unit elementand a unit-regular element. A ring R is called a clear ring if all elements in R are clearelements. In this paper, we study the new properties of clear elements in a ring andclear properties in certain special rings, such as opposite rings, quotient rings, cornerrings, Morita rings, and group rings.
Co-Authors Farizi, Salman Nikken Prima Puspita PERMATASARI, C. NOVITA SUBASTIAN, NANDA Suryoto Suryoto