JP Journal of Algebra, Number Theory and Applications
Volume 41, Issue 1, Pages 49 - 57
(January 2019) http://dx.doi.org/10.17654/NT041010049 |
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PURE CLOSED SUBOBJECTS AND PURE QUOTIENT GOLDIE DIMENSION
Mustafa Kemal Berktaş, Semra Doğruöz and Azime Tarhan
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Abstract: In this note we introduce pure closed subobjects, strongly pure closed subobjects and pure quotient Goldie dimension in finitely accessible additive categories. Then we give a generalization of a classical dimension formula with respect to their pure closed subobjects. We prove that in this category every strongly pure closed subobject of a pure quotient finite dimensional object of every class of objects closed under direct limits and pure epimorphic images has a semilocal endomorphism ring. |
Keywords and phrases: closed submodule, pure closed subobject, pure Goldie dimension, pure quotient Goldie dimension.
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