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A Generalization of Baer's Lemma

Molly Dunkum (2009)

Czechoslovak Mathematical Journal

There is a classical result known as Baer’s Lemma that states that an R -module E is injective if it is injective for R . This means that if a map from a submodule of R , that is, from a left ideal L of R to E can always be extended to R , then a map to E from a submodule A of any R -module B can be extended to B ; in other words, E is injective. In this paper, we generalize this result to the category q ω consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma...

A generalized minimal realization theory of machines in a category.

Antonio Bahamonde (1983)

Stochastica

This paper presents a generalized minimal realization theory of machines in a category which contains the Kleiski case. The minimal realization is the cheapest realization for a given cost functor. The final reachable realization of Arbib and Manes ([5]) and the minimal state approach for nondeterministic machines are included here.

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