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- W2538217026 abstract "ABSTRACTWe say that a class 𝒫 of right modules over a fixed ring R is an epic class if it is closed under homomorphic images. For an arbitrary epic class 𝒫, we define a 𝒫-dimension of modules that measures how far modules are from the modules in the class 𝒫. For an epic class 𝒫 consisting of indecomposable modules, first we characterize rings whose modules have 𝒫-dimension. In fact, we show that every right R-module has 𝒫-dimension if and only if R is a semisimple Artinan ring. Then we study fully Hopfian modules with 𝒫-dimension. In particular, we show that a commutative ring R with 𝒫-dimension (resp. finite 𝒫-dimension) is either local or Noetherian (resp. Artinian). Finally, we show that Matm(R) is a right Kothe ring for some m if and only if every (left) right module is a direct sum of modules of 𝒫-dimension at most n for some n, if and only if R is a pure semisimple ring." @default.
- W2538217026 created "2016-10-28" @default.
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- W2538217026 date "2016-10-21" @default.
- W2538217026 modified "2023-09-23" @default.
- W2538217026 title "Some new dimensions of modules and rings" @default.
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- W2538217026 doi "https://doi.org/10.1080/00927872.2016.1236389" @default.
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