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Research Article Open access CC BY 3.0

Note on Algebras that are Sums of Two Subalgebras Satisfying Polynomial Identities

Marek Kȩpczyk

Journal of Advances in Mathematics and Computer Science · pp. 3245–3251 · Published 16 Sep 2014

10.9734/BJMCS/2014/12652

Abstract

 We study an associative algebra A over an arbitrary field, that is a sum of two subalgebras B and C (i.e. A = B+C). We prove that if B has a nil ideal of bounded index, and that C has a commutative ideal, both of finite codimension in B and C, respectively, then for some nil PI ideal I of A the ring A/I has a commutative ideal of finite codimension.

Rings with polynomial identities prime rings.

References (10)

  1. 1 Polynomial Identities in Ring Theory [DOI]
  2. 2 Prime Rings Satisfying a Polynomial Identity [DOI]
  3. 3 Generalized polynomial identities and rings which are sums of two subrings [DOI]
  4. 4 Zur Nilpotenz gewisser assoziativer Ringe [DOI]
  5. 5 Identities of sums of commutative subalgebras [DOI]
  6. 6 On radicals of rings which are sums of two subrings [DOI]
  7. 7 RINGS WHICH ARE SUMS OF TWO SUBRINGS SATISFYING POLYNOMIAL IDENTITIES [DOI]
  8. 8 Rings which are sums of two subrings [DOI]
  9. 9 The sum of nil one-sided ideals of bounded index of a ring [DOI]
  10. 10 Nil 𝑃𝐼-rings [DOI]

Cited by 4

Note on algebras which are sums of two PI subalgebras

Marek Kȩpczyk · Journal of Algebra and Its Applications · 2015

A Note on Algebras that are Sums of Two Subalgebras

Marek Kępczyk · Canadian Mathematical Bulletin · 2016

Showing 2 of 4 known citations — external sources report more than can currently be individually listed.

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