Affiliation:
1. Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15–351 Białystok, Poland
Abstract
We study an associative algebra A over an arbitrary field that is a sum of two subalgebras A1 and A2 (i.e. A = A1 + A2). Additionally we assume that Ai has an ideal of finite codimension in Ai which satisfies a polynomial identity fi = 0 for i = 1, 2. Suppose that all rings R = R1 + R2, which are sums of subrings R1 and R2, are PI rings when Ri satisfies the polynomial identity fi = 0 for i = 1, 2. We prove that A is a PI algebra.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
9 articles.
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1. On the representation of fields as sums of two proper subfields;International Journal of Algebra and Computation;2024-08-10
2. On rings which are sums of subrings and additive subgroups;International Journal of Algebra and Computation;2022-06-21
3. Note on rings which are sums of a subring and an additive subgroup;Applicable Algebra in Engineering, Communication and Computing;2021-01-06
4. On the Representation of Fields as Finite Sums of Proper Subfields;Results in Mathematics;2020-04
5. Rings which are sums of PI subrings;Journal of Algebra and Its Applications;2019-08-05