Results 151 to 160 of about 1,144,675 (186)

Krull dimension in BL-algebra

Journal of Intelligent & Fuzzy Systems, 2014
In this paper, we introduce the notion of upper (down) set in BL-algebras and extended upper sets of BL-algebras. Also, the notions of Krull dimension and regular sequence in BL-algebras are introduced and studied in detail.
Mahdieh Abbasloo, Arsham Borumand Saeid
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A Generalization of the Classical Krull Dimension for Modules

Journal of Algebra, 2006
Let \(R\) be a ring with identity element. The aim of this paper is to define and investigate the classical Krull dimension \(\text{Cl.K.dim}(M)\) of an arbitrary left \(R\)-module \(M\). This concept, generalizing the concept of classical Krull dimension of a ring, is defined by means of chains of prime submodules of \(M\) and the following relation \(
Mahmood Behboodi
exaly   +2 more sources

The Transfer of the Krull Dimension and the Gabriel Dimension to Subidealizers

Canadian Journal of Mathematics, 1977
Let M be a right ideal of the ring T with identity. A unital subring R of T which contains M as a two-sided ideal is called a subidealizer ; the largest such subring is the idealizer I (M) of M in T. M is said to be generative if TM = T. In this case M is idempotent, and it follows from the dual basis lemma that T is finitely generated projective as a ...
Krause, Günter, Teply, Mark L.
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On Krull dimension of ore extensions

Georgian Mathematical Journal, 1996
This article studies the Krull dimension (Kdim), in the sense of Gabriel and Rentschler, of skew polynomial rings \(S=R[x;\alpha,\delta]\), where \(\alpha\) is an automorphism of \(R\) and \(\delta\) an \(\alpha\)-derivation. The main result is that if \(R\) is left Noetherian, \(\delta\) is nilpotent, say \(\delta^d=0\), and \(1_R\in\text{Im }\delta^i\
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On the Krull Dimension of Rings of Transfer Functions

Acta Applicandae Mathematicae, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amol Sasane
exaly   +3 more sources

Rings with Krull Dimension

1987
The aim of this section is to establish that a nil ideal of a ring with Krull dimension is nilpotent.
Constantin Nǎstǎsescu, Freddy van Oystaeyen   +1 more
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Global dimension of rings with krull dimension

Communications in Algebra, 1992
The left global dimension of a semiprime ring, with left Krull dimension α≥1 is found to be the supremum of the projective dimensions of the p-critical cyclic modules where β≤α. A similar result is true for upper triangular matrix rings whose entries come from a domain with Krull dimension.
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A krull-like dimension for noncommutative rings

Israel Journal of Mathematics, 1974
LetR be an associative ring. Using chains of prime torsion theories over the category of unitary leftR-modules, a generalization of the Krull dimension for commutative rings is defined and its properties investigated.
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Bézout Rings with Finite Krull Dimension

Journal of Mathematical Sciences, 2017
The main result of this paper is that if \(R\) is a commutative Bézout ring of Krull dimension 1, with stable range 2, then \(R\) is an elementary divisor ring, which generalizes some known results in [\textit{J. W. Brewer} et al., Commun. Algebra 12, 2987--3003 (1984; Zbl 0571.13004)] and [\textit{T. S. Shores}, Proc. Am. Math. Soc. 46, 211--213 (1974;
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Noetherian Rings with Krull Dimension One

Journal of the London Mathematical Society, 1977
One of the most challenging open problems in the theory of (left and right) noetherian rings is whether or not Jacobson's conjecture is valid, i.e. whether or not the intersection of the finite powers of the Jacobson radical is zero. In recent years an affirmative answer was given for fully bounded noetherian rings by \textit{A.
openaire   +1 more source