scholarly journals On a problem by Beidar concerning the central closure

2008 ◽  
Vol 429 (4) ◽  
pp. 835-840 ◽  
Author(s):  
Mikhail Chebotar
Keyword(s):  
Central Closure

Structure of Rings with Involution Applied to Generalized Polynomial Identities

1975 ◽  
Vol 27 (3) ◽  
pp. 573-584 ◽  
Author(s):  
Louis Halle Rowen
Keyword(s):  
Structure Theory ◽  
Polynomial Identities ◽  
Generalized Polynomial ◽  
Rings With Involution ◽  
Generalized Polynomial Identities ◽  
Central Closure

In [14, §4], some theorems were obtained about generalized polynomial identities in rings with involution, but the statements had to be weakened somewhat because a structure theory of rings with involution had not yet been developed sufficiently to permit proofs to utilize enough properties of rings with involution. In this paper, such a theory is developed. The key concept is that of the central closure of a ring with involution, given in § 1, shown to have properties analogous to the central closure of a ring without involution. In § 2, the theory of primitive rings with involution, first set forth by Baxter-Martindale [5], is pushed forward, to enable a setting of generalized identities in rings with involution which can parallel the non-involutory situation.

scholarly journals On polynomial rings over nil rings in several variables and the central closure of prime nil rings

2017 ◽  
Vol 223 (1) ◽  
pp. 309-322 ◽  
Author(s):  
M. Chebotar ◽  
W.-F. Ke ◽  
P.-H. Lee ◽  
E. R. Puczyłowski
Keyword(s):  
Polynomial Rings ◽  
Several Variables ◽  
Central Closure

Localization of modules and the central closure of rings

1981 ◽  
Vol 9 (14) ◽  
pp. 1455-1493 ◽  
Author(s):  
Robert Wisbauer
Keyword(s):  
Central Closure

Totally multiplicatively prime algebras

2002 ◽  
Vol 132 (5) ◽  
pp. 1145-1162
Author(s):  
M. Cabrera ◽  
Amir A. Mohammed
Keyword(s):  
Associative Algebras ◽  
Central Closure ◽  
The Stability ◽  
Multiplication Algebra

We introduce the totally multiplicatively prime algebras as those normed algebras for which there exists a positive number K such that K‖F‖‖a‖ ≤ ‖WF,a‖ for all F in M(A) (the multiplication algebra of A) and a in A, where WF,a denotes the operator from M(A) into A defined by WF,a(T) = FT(a) for all T in M(A). These algebras are totally prime and their multiplication algebra is ultraprime. We get the stability of the class of totally multiplicatively prime algebras by taking central closure. We prove that prime H*-algebras are totally multiplicatively prime and that the ℓ1-norm is the only classical norm on the free non-associative algebras for which these are totally multiplicatively prime.

scholarly journals Extended centroids of power series rings

1990 ◽  
Vol 32 (3) ◽  
pp. 371-375 ◽  
Author(s):  
W. S. Martindale ◽  
M. P. Rosen ◽  
J. D. Rosen
Keyword(s):  
Prime Ring ◽  
Polynomial Identity ◽  
Extended Centroid ◽  
Prime Rings ◽  
Generalized Polynomial ◽  
Ring Of Quotients ◽  
Power Series Rings ◽  
Central Simple ◽  
Generalized Polynomial Identity ◽  
Central Closure

Prime rings came into prominence when Posner characterized prime rings satisfying a polynomial identity [9]. The scarcity of invertible central elements made it difficult to generalize results from central simple and primitive algebras to prime rings. For example, we do not automatically have tensor products at our disposal. In [5], the first author introduced the Martindale ring of quotients Q(R) of a prime ring R in his theorem characterizing prime rings satisfying a generalized polynomial identity (GPI). Q(R) is a prime ring containing R whose center C is a field called the extended centroid of R. The central closure of R is the subring RC of Q(R) generated by R and C. RC is a closed prime ring since its extended centroid equals its center C. Hence we have a useful procedure for proving results about an arbitrary prime ring R. We first answer the question for closed prime rings and then apply to R the information obtained from RC. It should be noted that simple rings and free algebras of rank at least 2 are closed prime rings. For these reasons, closed prime rings are natural objects to study.

scholarly journals On prime rings whose central closure is finitely generated

2017 ◽  
Vol 488 ◽  
pp. 282-289
Author(s):  
M. Chebotar ◽  
W.-F. Ke ◽  
P.-H. Lee ◽  
E.R. Puczyłowski
Keyword(s):  
Finitely Generated ◽  
Prime Rings ◽  
Central Closure

On Identities with Composition of Generalized Derivations

2017 ◽  
Vol 60 (4) ◽  
pp. 721-735 ◽  
Author(s):  
Münevver Pınar Eroglu ◽  
Nurcan Argaç
Keyword(s):  
Prime Ring ◽  
Generalized Derivation ◽  
Multilinear Polynomial ◽  
Extended Centroid ◽  
Generalized Derivations ◽  
Ring Of Quotients ◽  
Central Closure

AbstractLet R be a prime ring with extended centroid C, Q maximal right ring of quotients of R, RC central closure of R such that dim C(RC) > , ƒ (X1, . . . , Xn) a multilinear polynomial over C that is not central-valued on R, and f (R) the set of all evaluations of the multilinear polynomial f (X1 , . . . , Xn) in R. Suppose that G is a nonzero generalized derivation of R such that G2(u)u ∈ C for all u ∈ ƒ(R).

Extended centroid and central closure of semiprime normed algebras. a first approach

1990 ◽  
Vol 18 (7) ◽  
pp. 2293-2326 ◽  
Author(s):  
M. Cabrera Garcia ◽  
A. Rodriguez Palacios
Keyword(s):  
Extended Centroid ◽  
Central Closure
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