SOME PROPERTIES OF CLEAR RINGS - Yassin Dwi Cahyo; C. NOVITA PERMATASARI; NANDA SUBASTIAN; SALMAN FARIZI; NIKKEN PRIMA PUSPITA; SURYOTO SURYOTO (Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang, 2026)
Let (R, +, ·) 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.