PURE CLOSED SUBOBJECTS AND PURE QUOTIENT GOLDIE DIMENSION

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.