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Two direct-summands  A  and  B  of a right  R -module  M  will be called strongly-perspective ( s -perspective) if for anyiffThe 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.

Perspectivity, exchange and summand-dual-square-free modules