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Triangular matrix algebras over Hensel rings


Author: Joseph A. Wehlen
Journal: Proc. Amer. Math. Soc. 37 (1973), 69-74
MSC: Primary 16A60
DOI: https://doi.org/10.1090/S0002-9939-1973-0308196-0
MathSciNet review: 0308196
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Abstract: Let (R, m) be a local Hensel ring and A an algebra over R which is finitely generated and projective as an R-module. If A contains a complete set of mutually orthogonal primitive idempotents $ {e_1}, \cdots ,{e_n}$ indexed so that $ {e_i}N{e_j} \subseteq mA$ whenever $ i \geqq j$, we show that A is isomorphic to a generalized triangular matrix algebra and that A is the epimorphic image of a finitely generated, projective R-algebra B of Hochschild dimension less than or equal to one.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0308196-0
Keywords: Hochschild dimension, cohomological dimension, generalized triangular matrix algebra, Hensel ring, maximal algebra, lifting idempotents
Article copyright: © Copyright 1973 American Mathematical Society

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