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Properties of fuzzy relations powers

Józef Drewniak, Barbara Pȩkala (2007)

Kybernetika

Properties of sup - * compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider sup - * powers of fuzzy relations under diverse assumptions about * operation. At first, we remind fundamental properties of sup - * composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined....

Properties of G-atoms and full Galois covering reduction to stabilizers

Piotr Dowbor (2000)

Colloquium Mathematicae

Given a group G of k-linear automorphisms of a locally bounded k-category R it is proved that the endomorphism algebra E n d R ( B ) of a G-atom B is a local semiprimary ring (Theorem 2.9); consequently, the injective E n d R ( B ) -module ( E n d R ( B ) ) * is indecomposable (Corollary 3.1) and the socle of the tensor product functor - R B * is simple (Theorem 4.4). The problem when the Galois covering reduction to stabilizers with respect to a set U of periodic G-atoms (defined by the functors Φ U : B U m o d k G B m o d ( R / G ) and Ψ U : m o d ( R / G ) B U m o d k G B )is full (resp. strictly full) is studied...

Prüfer rings with involution

Ismail M. Idris (2003)

Czechoslovak Mathematical Journal

The concept of a Prüfer ring is studied in the case of rings with involution such that it coincides with the corresponding notion in the case of commutative rings.

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