On the Classes of Almost (Dual) Perspective Modules
Vietnam Journal of Mathematics, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Publication Date: 2026
- Doi Number: 10.1007/s10013-026-00821-x
- Journal Name: Vietnam Journal of Mathematics
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: a-perspective module, ad-perspective module, Perspective module, Quivers and representations
- Hacettepe University Affiliated: Yes
Abstract
In this paper, we prove that s-perspective, a-perspective and ad-perspective conditions are equivalent conditions, for finite dimensional left R-modules, where R is an K-algebra. We construct more examples of s-perspective modules and hence a-perspective modules which do not have essentially unique direct complements. We introduce a stronger variation of s-perspective modules named as ss-perspective. Let R be any ring and let M be any left R-module. We will say that M is ss-perspective if for any isomorphic two direct summands A and B of M, the equalities M=A⊕X=B⊕Y imply that A=B or X=Y. We prove that the class of ss-perspective modules is contained properly in the class of s-perspective modules. We also prove that for commutative rings, s-perspectivity and ss-perspectivity coincide. Finally, we prove that for a left R-module M with S=EndR(M), if SS is ss-perspective then M is ss-perspective, while we prove that if SS is ss-perspective and M is weak duo, then M is ss-perspective.