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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Derivation modules of free joins and $m$-adic completions of algebras
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by I. Y. Chung PDF
Proc. Amer. Math. Soc. 34 (1972), 49-56 Request permission

Abstract:

A free commutative join of subalgebras corresponds to a direct sum of submodules in a universal derivation module. In particular, indeterminates of a polynomial ring correspond to elements of a linearly independent set in a universal derivation module. As an application, a simple proof of the uniqueness of cardinalities of indeterminates of a polynomial ring can be obtained by using that of linear bases of a free module over a commutative ring. Similar observations are made for $\mathfrak {m}$-adic completions of algebras and their derivation modules. Also, the module of linear differential forms of an $\mathfrak {m}$-adic completion of an algebra is studied.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 49-56
  • MSC: Primary 13B10
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0296061-6
  • MathSciNet review: 0296061