Embeddings in matrix wreath products of algebras

2021 ◽  
Author(s):  
Adel Alahmadi ◽  
Hamed Alsulami ◽  
S. K. Jain ◽  
Efim Zelmanov
Keyword(s):  
Commutative Algebra ◽  
Wreath Products ◽  
Finitely Generated ◽  
Infinite Dimensional ◽  
Algebra 2

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.

scholarly journals Progress in Commutative Algebra 2

2012 ◽  
Author(s):  
Jason G. Boynton ◽  
Ela Celikbas ◽  
Scott T. Chapman ◽  
Jim Coykendall ◽  
Florian Enescu ◽  
...  
Keyword(s):  
Commutative Algebra ◽  
Algebra 2

scholarly journals EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS

2021 ◽  
pp. 1-66
Author(s):  
Tom Bachmann ◽  
Kirsten Wickelgren
Keyword(s):  
Commutative Algebra ◽  
Vector Bundles ◽  
Euler Class ◽  
Complete Intersections ◽  
Bilinear Forms ◽  
Euler Numbers ◽  
Coherent Sheaves ◽  
Linear Subspaces ◽  
Algebraic Vector

Abstract We equate various Euler classes of algebraic vector bundles, including those of [12] and one suggested by M. J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class and give formulas for local indices at isolated zeros, both in terms of the six-functors formalism of coherent sheaves and as an explicit recipe in the commutative algebra of Scheja and Storch. As an application, we compute the Euler classes enriched in bilinear forms associated to arithmetic counts of d-planes on complete intersections in $\mathbb P^n$ in terms of topological Euler numbers over $\mathbb {R}$ and $\mathbb {C}$ .

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