Generalized polynomial identities and rings which are sums of two subrings

1995 ◽  
Vol 34 (1) ◽  
pp. 1-5 ◽  
Author(s):  
K. I. Beidar ◽  
A. V. Mikhalev
Keyword(s):  
Polynomial Identities ◽  
Generalized Polynomial ◽  
Generalized Polynomial Identities

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.

A Note on Generalized Polynomial Identities

1972 ◽  
Vol 15 (4) ◽  
pp. 605-606 ◽  
Author(s):  
Wallace S. Martindale
Keyword(s):  
Free Product ◽  
Free Algebra ◽  
Polynomial Identities ◽  
Generalized Polynomial ◽  
Generalized Polynomial Identities

Let A be an algebra with 1 over a field F and let B be a fixed F-basis of A. Let F〈x〉=F〈x1,…, xn,…,〉 be the free algebra over F in noncommutative indeterminates x1,…, xn,…, and denote by AF〈x〉 the free product of A and F〈x〉 over F. The elements of AF〈x〉 of the form varies, repetitions allowed) form an F-basis of AF〈x〉. They will be referred to as basis monomials, and the involved in a particular basis monomial will be called the coefficients of that basis monomial.

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