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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Jurnal Matematika UNAND
Yassin Dwi Cahyo
Universitas Diponegoro
Computer Science & IT Mathematics

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SOME PROPERTIES OF CLEAR RINGS Yassin Dwi Cahyo; C. NOVITA PERMATASARI; NANDA SUBASTIAN; SALMAN FARIZI; NIKKEN PRIMA PUSPITA; 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.
Exact Sequences in (R,S)-Modules Dian Ariesta Yuwaningsih; Yassin Dwi Cahyo; Nanda Subastian
Jurnal Matematika, Statistika dan Komputasi Vol. 23 No. 1 (2026): September 2026
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/ersnw733

Abstract

The concept of modules has been generalized to the structure of (R,S)-bimodules, which has further been extended to (R,S)-modules. Various properties of classical module theory have been developed within the framework of (R,S)-modules. One of the important topics in module theory that can be extended to this setting is the concept of exact sequences. In this paper, we develop the notion of exact sequences in modules to exact sequences in (R,S)-modules. We begin by introducing the definitions of exact sequences and short exact sequences in (R,S)-modules and examine their basic properties. Several examples are provided to illustrate the concepts and to highlight the similarities and differences with classical module theory. In addition, we establish criteria for determining when a short exact sequence of (R,S)-modules splits and present related structural results using commutative diagrams. Furthermore, we present the necessary and sufficient conditions for an (R,S)-module to be Noetherian in a short exact sequence. These results contribute to a deeper understanding of the homological behavior of -modules and provide a foundation for further research in this area.
Co-Authors C. NOVITA PERMATASARI Dian Ariesta Yuwaningsih Nanda Subastian NANDA SUBASTIAN Nikken Prima Puspita Salman Farizi Suryoto Suryoto