Title: Embeddings in Matrix Wreath Products of Algebras
Speaker: S. K. Jain (Ohio University, Athens)
Abstract: 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 $A$ there exists an epimorphism $\widehat A\overset{\varphi}{\to }A$, where $(\ker\varphi)^3=(0)$ and the algebra $\widehat A$ is not representable by matrices over a commutative algebra. If the algebra $A$ is commutative, then $\widehat A$ satisfies the ACC on two-sided ideals as in the recent examples of B. Greenfeld and L.H. Rowen..( References: Alahmadi-Alsulami-Jain-Zelmanov, Trans AMS (2019); Alahmadi-Alsulami-Jain-Zelmanov, JAA(2021); B.Stenstrom. Rings of Quotients), Springer; K. Goodearl, Nonsingular Rings, Marcel Dekker.)
Zoom: https://osu.zoom.us/j/92105949811?pwd=UDNtZ2dubFd5VFI3bDRINGNoZkdxQT09
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