Dualities in modules and the AB5* condition

Brodskii, G. M.

doi:10.1070/rm1983v038n02abeh003474

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* Partially Supported By the Russian Foundation For Fundamen1

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1996

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“…• This theorem has been reported at Moscow University [5], and has been announced in [6]. Among consequences of the theorem there are "Existence Theorem" from [7], Theorem 6 and Corollary 1 from [8], Theorem 13 from [9] and other well-known results.…”

Section: * Partially Supported By the Russian Foundation For Fundamenmentioning

confidence: 90%

Lattice anti-isomorphisms of modules and the AB5* condition

Brodskii¹,

Fong²,

Knauer³

et al. 1996

First International Tainan-Moscow Algebra Workshop

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All rings considered in this paper are associative with an identity element and all modules are unitary. Homomorphisms of right modules will be wirtten on the left hand side. We shall use the following notation: L* is the dual of a partially ordered set L; End(X) and L(X) are the endomorphism ring and the submodule lattice of a module X.We recall some definitions and results. An element c of a complete lattice L isthere exists do e D such that c = do-A complete lattice L is called (weakly) algebraic if every element in L is a join of (weakly) compact elments. A complete lattice L is called upper continuous if a /\ (V

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