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- W4200480348 abstract "Two direct-summands A and B of a right R-module M will be called strongly-perspective (s-perspective) if for any X⊆M, M=A ⊕ X iff M=B ⊕ X. The module M will be called s-perspective if every two isomorphic direct-summands of M are s-perspective, and a ring R will be called s-perspective if R as a right R-module is s-perspective. In this paper, we study s-perspective rings and modules, and using ideas of Khurana and Nielsen, it follows that if M is s-perspective, then M has the finite exchange property iff M is clean, iff M has the full exchange property. In particular, if M is either summand-square-free or dual-summand-square-free with the finite exchange property, then M is clean, s-perspective and has the full exchange property." @default.
- W4200480348 created "2021-12-31" @default.
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- W4200480348 date "2021-12-16" @default.
- W4200480348 modified "2023-10-14" @default.
- W4200480348 title "Perspectivity, exchange and summand-dual-square-free modules" @default.
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- W4200480348 doi "https://doi.org/10.1080/00927872.2021.2008414" @default.
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