Embeddings in matrix wreath products of algebras
Keyword(s):
We use matrix wreath products to show that (1) every countable dimensional nonsingular algebra is embeddable in a finitely generated nonsingular algebra, (2) for every infinite dimensional finitely generated PI-algebra [Formula: see text] there exists an epimorphism [Formula: see text], where [Formula: see text] and the algebra [Formula: see text] is not representable by matrices over a commutative algebra. If the algebra [Formula: see text] is commutative, then [Formula: see text] satisfies the ACC on two-sided ideals as in the recent examples of Greenfeld and Rowen.
2009 ◽
Vol 19
(03)
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pp. 287-303
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2008 ◽
Vol 60
(5)
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pp. 1001-1009
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Keyword(s):
2019 ◽
Vol 62
(3)
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pp. 733-738
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Keyword(s):
2018 ◽
Vol 17
(02)
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pp. 1850023
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Finitely generated ideals in certain algebras of transfer functions for infinite-dimensional systems
1987 ◽
Vol 45
(1)
◽
pp. 247-250
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Keyword(s):
2020 ◽
Vol 23
(1)
◽
pp. 479-483