/pdf/separate-continuity-and-joint-continuity-1wlhvewj3i.pdf

Separate continuity and joint continuity

The quotient category of a Morita context

/pdf/squares-in-some-recurrent-sequences-34p0k8cm9d.pdf

Squares in some recurrent sequences.

/pdf/regular-completions-of-cauchy-spaces-3so291wjg6.pdf

Regular completions of Cauchy spaces

/pdf/an-adjunction-theorem-for-locally-equiconnected-spaces-2xyhmm7mj4.pdf

An adjunction theorem for locally equiconnected spaces

This paper investigates two related problems. The first is to describe the double centralizer of an arbitrary projective right iϋ-modiile. This proves to be the ring of left quotients of R with respect to a certain canonical hereditary torsion class of left ϋί-modules determined by the projective module. The second is to determine the relationship between rings of left quotients of R and S, where S is the endomorphism ring of a finitely generated projective right ϋί-module PR. It is shown that there exists an inclusion-preserving, one-to-one correspondence between hereditary torsion classes (or localizing subcategories) of left ^-modules and hereditary torsion classes of left E-modules which contain the canonical torsion class determined by PR. If QR and Qs are rings of left quotients with respect to corresponding classes, then P($$RQR is a finitely generated projective right Q^-module with Qs as its Q#-endomorphism ring. Necessary and sufficient conditions are obtained for the maximal rings of left quotients to be related in this manner. In particular, this occurs when PR is a faithful .R-module and R is either a semi-prime ring or a ring with zero left singular ideal. The situation considered includes the case where S is an arbitrary ring, SP is a left ^-generator, and R is the Sendomorphism ring of SP When SP is a projective left Sgenerator, the maximal rings of left quotients of R and S are related in the manner considered above.

/pdf/rings-of-quotients-of-endomorphism-rings-of-projective-1yfxl1lypv.pdf

Rings of quotients of endomorphism rings of projective modules.

Of the several types of noncommutativ e quotient rings, finite left localizations have structure most like that of the original ring. This paper examines finite left localizations from two points of view: As rings of quotients with respect to hereditary torsion classes, and as endomorphism rings of finitely generated projective modules. In the first case, finite left localizations are shown to be the rings of quotients with respect to perfect TTF-classes. In the second, they are shown to be the double centralizers of finite projectors. The first characterization (Corollary 1.2) shows that finite left localizations may be realized as endomorphism rings of finitely generated projective idempotent ideals. It follows that every left localization of a right perfect ring is finite. Finally, the finite projectors of the second characterization (Corollary 2.2) are shown to have endomorphism rings whose quotient ring structure is very closely related to that of the original ring. For example, every ring of left quotients of the endomorphism ring is Morita equivalent to a ring of quotients of the original ring.

/pdf/on-finite-left-localizations-2i0jkjmakv.pdf

On finite left localizations.

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Rings of quotients of endomorphism rings of projective modules.

On finite left localizations.