Titlebook: Serial Rings; Gennadi Puninski Book 2001 Springer Science+Business Media Dordrecht 2001 Finite.Morphism.algebra.commutative property.endom

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Basic Notions,Let the rings under consideration be assumed to be associative with unit and all the modules be unitary and almost everywhere right. So we shall write the homomorphisms of right (left) modules from the left (right).

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Classical Localizations in Serial Rings,In this section we show that ‘almost all’ classical localizations in a serial ring are the localizations at a semi-prime Goldie ideal. For an ideal . of a ring . by .(.) we denote the set of elements of . whose images are nonzero divisors in ..

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Serial Prime Goldie Rings,Let us recall that . = Jac(.), . = 1,..., ..

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大范围流行

Indecomposable Pure Injective Modules over Serial Rings,Let . be an indecomposable idempotent of a serial ring .. A pp-type .(.) is called an . if . | . ∈ .; and pp-formula .(.) is an . if . → . | .. For example, the pp-formula . | . for . ∈ . is an .-formula. A . is a pair 〈., .〉, where . ⊂ . is a right ideal and . ⊂ . is a left ideal of ..

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Super-Decomposable Pure Injective Modules over Commutative Valuation Rings,A module . is called . if it contains no indecomposable direct summand. In particular, . = . ⊕ ., . = . ⊕ ., . = . ⊕ . for nonzero ., and so on.

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Pure Injective Modules over Commutative Valuation Domains,In this section we classify in particular, pure injective modules .(.) over commutative valuation domains. But first let us recall some definitions and facts.

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Pure Projective Modules over Nearly Simple Uniserial Domains,First let us recall some results about a decomposition of projective modules and an equivalence of categories which will be used in the sequel.