2 results
ON GRADED SYMMETRIC CELLULAR ALGEBRAS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 108 / Issue 3 / June 2020
- Published online by Cambridge University Press:
- 29 July 2019, pp. 349-362
- Print publication:
- June 2020
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- Article
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Let
$A=\bigoplus _{i\in \mathbb{Z}}A_{i}$ be a finite-dimensional graded symmetric cellular algebra with a homogeneous symmetrizing trace of degree 
$d$. We prove that if 
$d\neq 0$ then 
$A_{-d}$ contains the Higman ideal 
$H(A)$ and 
$\dim H(A)\leq \dim A_{0}$, and provide a semisimplicity criterion for 
$A$ in terms of the centralizer of 
$A_{0}$.
Group Actions on Quasi-Baer Rings
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- Journal:
- Canadian Mathematical Bulletin / Volume 52 / Issue 4 / 01 December 2009
- Published online by Cambridge University Press:
- 20 November 2018, pp. 564-582
- Print publication:
- 01 December 2009
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- Article
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A ring
$R$ is called quasi-Baer if the right annihilator of every right ideal of $R$ is generated by an idempotent as a right ideal. We investigate the quasi-Baer property of skew group rings and fixed rings under a finite group action on a semiprime ring and their applications to 
${{C}^{*}}$-algebras. Various examples to illustrate and delimit our results are provided.
