Quasi-semi clean rings - H. Remzi, Esraa; Al-Sammarraie, Samer; El-Najjar, Abdelwahhab; S. Mohammed, Akram (Journal of Al-Qadisiyah for Computer Science and Mathematics, 2025)
Recently, Tang et al. [1] studied a broader concept than the concept of clean rings called quasi-clean rings. In this paper, we use the method of Tang et al. [1] in generalizing clean to construct and study a generalization of semiclean rings of Ye [3] to a broader class of rings called quasi-semiclean rings. Let be a ring with identity. Then, is said to be a quasi-semicelan ring if every element can be expressed as where is a unit of and is a quasi-periodic element of : that is satisfies the equation where and is a central unit, . We prove several properties of the class of quasi-semiclean rings similar to those of semiclean rings and also settle new properties and results. In particular, we show that clean rings and certain types of quasi-semiclean rings (quasi-clean rings to be precise) are the same concept and prove this equivalence. Furthermore, we investigate the quasi-semicleaness of various types of rings such as Morita context rings, trivial extensions of modules , and the Nagata ring .