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Nondegenerate cohomology pairing for transitive Lie algebroids, characterization

Jan Kubarski, Alexandr Mishchenko (2004)

Open Mathematics

The Evens-Lu-Weinstein representation (Q A, D) for a Lie algebroid A on a manifold M is studied in the transitive case. To consider at the same time non-oriented manifolds as well, this representation is slightly modified to (Q Aor, Dor) by tensoring by orientation flat line bundle, Q Aor=QA⊗or (M) and D or=D⊗∂Aor. It is shown that the induced cohomology pairing is nondegenerate and that the representation (Q Aor, Dor) is the unique (up to isomorphy) line representation for which the top group of...

Non-singular covers over monoid rings

Ladislav Bican (2008)

Mathematica Bohemica

We shall introduce the class of strongly cancellative multiplicative monoids which contains the class of all totally ordered cancellative monoids and it is contained in the class of all cancellative monoids. If G is a strongly cancellative monoid such that h G ⊆ G h for each h ∈ G and if R is a ring such that a R ⊆ R a for each a ∈ R , then the class of all non-singular left R -modules is a cover class if and only if the class of all non-singular left R G -modules is a cover class. These two conditions are also equivalent whenever...

Non-singular covers over ordered monoid rings

Ladislav Bican (2006)

Mathematica Bohemica

Let G be a multiplicative monoid. If R G is a non-singular ring such that the class of all non-singular R G -modules is a cover class, then the class of all non-singular R -modules is a cover class. These two conditions are equivalent whenever G is a well-ordered cancellative monoid such that for all elements g , h ∈ G with g < h there is l ∈ G such that l g = h . For a totally ordered cancellative monoid the equalities Z ( R G ) = Z ( R ) G and σ ( R G ) = σ ( R ) G hold, σ being Goldie’s torsion theory.

Non-singular precovers over polynomial rings

Ladislav Bican (2006)

Commentationes Mathematicae Universitatis Carolinae

One of the results in my previous paper On torsionfree classes which are not precover classes, preprint, Corollary 3, states that for every hereditary torsion theory τ for the category R -mod with τ ≥ σ , σ being Goldie’s torsion theory, the class of all τ -torsionfree modules forms a (pre)cover class if and only if τ is of finite type. The purpose of this note is to show that all members of the countable set 𝔐 = { R , R / σ ( R ) , R [ x 1 , ⋯ , x n ] , R [ x 1 , ⋯ , x n ] / σ ( R [ x 1 , ⋯ , x n ] ) , n < ω } of rings have the property that the class of all non-singular left modules forms a (pre)cover...

Normalisation of the Theory T of Cartesian Closed Categories and Conservativity of Extensions T[x] of T

Anne Preller, P. Duroux (2010)

RAIRO - Theoretical Informatics and Applications

Using an inductive definition of normal terms of the theory of Cartesian Closed Categories with a given graph of distinguished morphisms, we give a reduction free proof of the decidability of this theory. This inductive definition enables us to show via functional completeness that extensions of such a theory by new constants (“indeterminates”) are conservative.

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