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 -