ZSn-Modules and polynomial identities with integer coefficients
(2013) International Journal of Algebra and Computation — Vol. 23, n° 8, p. 1925-1943 (2013)
Files
integralcodimensions_GorJan.pdf
Published version
Open Access - Adobe PDF
- 269.53 KB
Details
- Authors
- Abstract
- We show that, like in the case of algebras over fields, the study of multilinear polynomial identities of unitary rings can be reduced to the study of proper polynomial identities. In particular, the factors of series of ZS n-submodules in the ZSn-modules of multilinear polynomial functions can be derived by the analog of Young's (or Pieri's) rule from the factors of series in the corresponding ZSn-modules of proper polynomial functions. As an application, we calculate the codimensions and a basis of multilinear polynomial identities of unitary rings of upper triangular 2 × 2 matrices and infinitely generated Grassmann algebras over unitary rings. In addition, we calculate the factors of series of ZSn- submodules for these algebras. Also we establish relations between codimensions of rings and codimensions of algebras and show that the analog of Amitsur's conjecture holds in all torsion-free rings, and all torsion-free rings with 1 satisfy the analog of Regev's conjecture. © 2013 World Scientific Publishing Company.
- Affiliations
Citations
Gordienko, A., & Janssens, G. (2013). ZSn-Modules and polynomial identities with integer coefficients. International Journal of Algebra and Computation, 23(8), 1925-1943. https://doi.org/10.1142/S0218196713500513 (Original work published 2013)