Results 141 to 150 of about 178 (166)

Jacobson rings with a polynomial identity

Communications in Algebra, 1988
Efraim P Armendáriz
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Rings with Involution and Polynomial Identities

Canadian Journal of Mathematics, 1968
An involution * of a ring A is a one-one additive mapping of A onto itself such that (xy)* = y*x* and x** = x for all x, y ∊ A. If A is an algebra over a field Φ, one makes the additional requirement that (λx)* = λx* for all λ ∊ Φ, x ∊ A. S will generally denote the set of symmetric elements s* = s, K the set of skew elements , and Z the centre of A.
Baxter, W. E., Martindale, W. S. III
openaire   +1 more source

Polynomial identities of related rings

Israel Journal of Mathematics, 1970
The set of polynomial identities of a ringA is considered, as well as some types of minimal identities. The change which occurs in these identities upon passage to related rings is then studied.
Leron, U., Vapne, A.
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A Version of Zariski's Main Theorem for Polynomial Identity Rings

American Journal of Mathematics, 1979
M Artin
exaly   +3 more sources

Rings with a polynomial identity

2011
Since Kaplansky's first paper on the subject of P.I. rings appeared in 1948, many fruitful results have arisen from the study of such rings. This thesis attempts to present the most important of these results in a unified theory. Chapter I gives the basic notation, definitions, a number of small lemmas together with Kaplansky's incisive result on ...
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Jacobson - rings and hilbert algebras with polynomial identities

Annali di Matematica Pura ed Applicata, 1966
We consider n-tuples of m × m matrices as zeroes of non-commutative polynomials in n-variables and establish an analogue of the classical Hilbert-Nullstellensatz. We study then finitely generated non-commutative algebras over Jacobson rings and obtain results conpletely analogous with the commutative tehory.
Amitsur, S. A., Procesi, C.
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Skew Polynomial Rings Satisfying a Polynomial Identity

2002
In this short appendix, we prove a result of Jondrup on the PI degree of skew polynomial algebras in characteristic 0, and illustrate its relevance in the settings of interest in these notes. Exceptionally, we make use in this section of a few lemmas from Part II.
Ken A. Brown, Ken R. Goodearl
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First-order rigidity of rings satisfying polynomial identities

Annals of Pure and Applied Logic, 2022
One of the most fundamental questions in model theory is to what extent the first-order theory of a given model determines its isomorphism class. A finitely generated algebraic structure is said to be \textit{ first-order rigid} if its elementary theory determines its isomorphism class among finitely generated models.
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Noetherian rings and polynomial identities

2003
The Artinian condition on rings leads to a very satisfactory theory, at least in the semisimple case, yet it excludes such familiar examples as the ring of integers. This ring is included in the wider class of Noetherian rings, which has been much studied in recent years.
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Azumaya algebras and rings with polynomial identity

Mathematical Proceedings of the Cambridge Philosophical Society, 1976
The Formanek polynomial gives an explicit expression for the calculation of central elements in a prime ring with polynomial identity, in such a form as to provide a set of linear maps of the ring into its centre. This note makes use of properties of these maps with the object of giving a direct proof of the remarkable theorem of M.
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