Results 41 to 50 of about 99 (88)
SK1 of Azumaya algebras over Hensel pairs
, 2010 Let A be an Azumaya algebra of constant rank n2 over a Hensel pair (R, I) where R is a semilocal ring with n invertible in R. Then the reduced Whitehead group SK1(A) coincides with its reduction SK1(A/I A).
Hazrat, Roozbeh (R16959)
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A Generalized Primitive Element Theorem
, 2007 We deal with the following variant of the primitive element theorem: any commutative strongly separable extension of a commutative ring can be embedded in another one having primitive element.
Bagio, Dirceu, Paques, Antonio
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Direct-Sum Decompositions over Local Rings
, 2001 Let (R,m) be a local ring (commutative and Noetherian). If R is complete (or, more generally, Henselian), one has the Krull–Schmidt uniqueness theorem for direct sums of indecomposable finitely generated R-modules. By passing to the m-adic completion R̂,
Wiegand, Roger
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Parabolic subgroups of groups of column-finite infinite matrices
, 2012 For a wide class of rings R that contains all local and semilocal rings, we consider the group SLVK(R) of all matrices over R of the form ab0c, in which a is a finite matrix with determinant 1 and c is an upper triangular infinite matrix with the main ...
Słowik, Roksana, Hołubowski, Waldemar
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Pfister's local-global principle for Azumaya algebras with involution
, 2023 We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is $2$-primary torsion.
Astier, Vincent, Unger, Thomas
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On the primitivity of polynomial rings with nonprimitive coefficient rings
, 1986 For a hereditary noetherian prime ring R R with classical quotient ring Q Q , various necessary and sufficient conditions are given for the polynomial ring R [ X
T. J. Hodges
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Symmetric Forms over Semilocal Rings
, 2020 В работе рассматриваются симметричные матрицы, квадрики и квадратичные формы (включая вырожденные) над полулокальными кольцами.The necessary and sufficient conditions for congruence of quadratic forms over a local ring with a principal maximal ideal ...
Старикова, Ольга А. +1 more
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, 2005 It is proved that a ring R is right perfect if and only if it is Σ-cotorsion as a right module over itself. Several other conditions are shown to be equivalent. For example, that every pure submodule of a free right R-module is strongly pure-essential in
Guil Asensio, Pedro A., Herzog, Ivo
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Quadratic forms, orderings and quaternion algebras over rings with many units [PDF]
, 1988 The "algebraic" theory of quadratic forms over fields of characteristic ≠2 dates back to the 1937 paper of Witt [37]. It was in this paper that the Witt ring of a field was first considered.
Walter, Leslie J.
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On some classes of modules and their endomorphism rings
, 2014 In [33], it was proved that an injective module is indecomposable if and only if its endomorphism ring is local. The first aim of this thesis is to generalize this result from indecomposable modules to square-free ones by showing that an injective module
Bien, M.H.
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