Graded Modules as a Clean Comodule
Nikken Prima Puspita,
Indah Emilia Wijayanti and
Journal of Mathematics Research, 2020, vol. 12, issue 6, 66
In ring and module theory, the cleanness property is well established. If any element of R can be expressed as the sum of an idempotent and a unit, then R is said to be a clean ring. Moreover, an R-module M is clean if the endomorphism ring of M is clean. We study the cleanness concept of coalgebra and comodules as a dualization of the cleanness in rings and modules. Let C be an R-coalgebra and M be a C-comodule. Since the endomorphism of C-comodule M is a ring, M is called a clean C-comodule if the ring of C-comodule endomorphisms of M is clean. In Brzezi´nski and Wisbauer (2003), the group ring R[G] is an R-coalgebra. Consider M as an R[G]-comodule. In this paper, we have investigated some sucient conditions to make M a clean R[G]-comodule, and have shown that every G-graded module M is a clean R[G]-comodule if M is a clean R-module.
JEL-codes: R00 Z0 (search for similar items in EconPapers)
References: View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:12:y:2020:i:6:p:66
Access Statistics for this article
More articles in Journal of Mathematics Research from Canadian Center of Science and Education Contact information at EDIRC.
Bibliographic data for series maintained by Canadian Center of Science and Education ().