TY - JOUR

T1 - Structure of Zariski-closed algebras

AU - Belov-Kanel, Alexei

AU - Rowen, Louis

AU - Vishne, Uzi

PY - 2010/9

Y1 - 2010/9

N2 - The objective of this paper is to describe the structure of Zariskiclosed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a version of Wedderburn's principal theorem as well as a more explicit description using representations, in terms of "gluing" in Wedderburn components. Finally, we construct "generic" Zariski-closed algebras, whose description is considerably more complicated than the description of generic algebra of finite dimensional algebras. Special attention is given to infinite dimensional algebras over finite fields.

AB - The objective of this paper is to describe the structure of Zariskiclosed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a version of Wedderburn's principal theorem as well as a more explicit description using representations, in terms of "gluing" in Wedderburn components. Finally, we construct "generic" Zariski-closed algebras, whose description is considerably more complicated than the description of generic algebra of finite dimensional algebras. Special attention is given to infinite dimensional algebras over finite fields.

UR - http://www.scopus.com/inward/record.url?scp=77952086684&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-10-04993-7

DO - 10.1090/S0002-9947-10-04993-7

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AN - SCOPUS:77952086684

SN - 0002-9947

VL - 362

SP - 4695

EP - 4734

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 9

ER -