Results 61 to 70 of about 99 (88)
Direct-sum decompositions over local rings
, 2008 . 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
Roger Wiegand
core
Real closures of semilocal rings, and extension of real places [PDF]
Bulletin of the American Mathematical Society, 1973 openaire +4 more sources
Locally compact equicharacteristic semilocal rings
Duke Mathematical Journal, 1968 openaire +2 more sources
A Generalized Primitive Element Theorem
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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Ranks and bounds for indecomposable modules over one-dimensional Noetherian rings
, 2007 We consider one-dimensional, reduced Noetherian rings R with finite normalization. We assume that there exists a positive integer NR such that, for every indecomposable finitely generated torsion-free R-module M and for every minimal prime ideal P of R,
Luckas, Melissa R
core
On the Theory of Multiplicities in Finite Modules over Semi-Local Rings
Hiroshima Mathematical Journal, 1959 openaire +3 more sources
Local Rings, Semilocal Rings, and Idempotents
Graduate Texts in Mathematics, 1991 In the first two sections of this chapter, we focus our attention on two special classes of rings, namely, local rings and semilocal rings. By definition, a ring R is local if R/rad R is a division ring, and R is semilocal if R/rad R is a semisimple ring.
T Y Lam, Lam T Y
exaly +5 more sources
Factorizations of elements in local rings and semilocal rings of finite type
Journal of Algebra and Its Applications, 2019 Factorizations of ring elements are described by finite chains of principal ideals. We use the description of cyclically presented modules over local rings to study factorization of elements in local rings.
Arroyo Paniagua María José +2 more
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Semilocal rings whose adjoint group is locally supersoluble
Archiv der Mathematik, 2010Let \(R\) be an associative ring, not necessarily with an identity element. Let \(R^{ad}\) be the adjoint semigroup of \(R\) under the operation \(a\circ b=a+b+ab\) for all \(a,b\in R\) with neutral element \(0\in R\). Let \(R^\circ\) be the adjoint group of \(R\), that is, the group of all invertible elements of the semigroup \(R^{ad}\).
CATINO, Francesco +2 more
openaire +2 more sources