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Let R be Noetherian normal domain. We shall call an R -algebra A quasi A ∗ if A = R ( X , ( a X + b ) − 1 ) where X ∈ A is a transcendental element over R , a ∈ R ∖ 0 , b ∈ R and ( a , b ) R = R . In this paper we shall describe a general structure for any faithfully flat R -algebra A...
We generalize the tilting process by Happel, Reiten and Smalø to the setting of finitely presented modules over right coherent rings. Moreover, we extend the characterization of quasi-tilted artin algebras as the almost hereditary ones to all right noetherian rings.
This paper proves that the winning strategy for Hauser’s version of Hironaka’s polyhedra game is almost arbitrary. The winning strategy and its associated invariants are based on an algorithm of matrix triangulations and matrix diagonalizations. It is proved that if a set sequence constitutes...
It is known that finite crossed modules provide premodular tensor categories. These categories are in fact modularizable. We construct the modularization and show that it is equivalent to the module category of a finite Drinfeld double.
Let F be an infinitely generated free group and let R be a fully invariant subgroup of F such that (a) R is contained in the commutator subgroup F ′ of F and (b) the quotient group F / R is residually torsion-free nilpotent. Then the automorphism group Aut ( F / R ′ ) of the group F / R ′...
For a commutative ring R , the F -signature was defined by Huneke and Leuschke (Math. Ann. 324 (2) (2002) 391–404). It is an invariant that measures the order of the rank of the free direct summand of R ( e ) . Here, R ( e ) is R itself, regarded as an R -module through e -times Frobenius...
We prove that four different notions of Morita equivalence for inverse semigroups motivated by C ∗ -algebra theory, topos theory, semigroup theory and the theory of ordered groupoids are equivalent. We also show that the category of unitary actions of an inverse semigroup is monadic over the...
Let S ( m | n , r ) Z be a Z -form of a Schur superalgebra S ( m | n , r ) generated by elements ξ i , j . We solve a problem of Muir and describe a Z -form of a simple S ( m | n , r ) -module D λ , Q over the field Q of rational numbers, under the action of S ( m | n , r ) Z . This Z -form is...
We study the mod 2 homology of the double and triple loop spaces of homogeneous spaces associated with exceptional Lie groups. The main computational tools are the Serre spectral sequence for fibrations Ω n + 1 G → Ω n + 1 ( G / H ) → Ω n H for n = 1 , 2 , and the Eilenberg–Moore...
We generalize Barr’s embedding theorem for regular categories to the context of enriched categories.
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