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Dergiler / Turkish Journal of Mathematics / 2015 / Cilt: 39 - Sayı: 2

Coextended weak entwining structures

Jos´e Nicanor ALVAREZ ALONSO, Jos´e Manuel VILABOA FERNANDEZ, Ramon RODRIGUEZ GONZALEZ

Sayfa
174–199
DOI
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Özet

In this paper, we formulate the definition of coextended weak entwining structure in a strict monoidal category with equalizers. For a coextended weak entwining structure (A,D,y,a), we introduce the notions of weak (D,a)-cleft extension and weak (D,a)-Galois extension (with normal basis), proving that weak (D,a)-Galois extensions with normal basis are equivalent to weak (D,a)-cleft extensions.

Abstract

In this paper, we formulate the definition of coextended weak entwining structure in a strict monoidal category with equalizers. For a coextended weak entwining structure (A,D,y,a), we introduce the notions of weak (D,a)-cleft extension and weak (D,a)-Galois extension (with normal basis), proving that weak (D,a)-Galois extensions with normal basis are equivalent to weak (D,a)-cleft extensions.

Anahtar kelimeler: Monoidal category, coextended weak entwining structure, weak cleft extension, weak Galois extension, normal basis