Coherence of polynomial rings over semisimple algebraic algebras

Carson, Andrew B.

doi:10.1090/S0002-9939-1972-0291216-9

Coherence of polynomial rings over semisimple algebraic algebras
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by Andrew B. Carson PDF

Proc. Amer. Math. Soc. 34 (1972), 20-24 Request permission

Abstract:

It is shown that polynomial rings in finitely or infinitely many central indeterminates, over a commutative algebraic algebra without nilpotent elements, are coherent. If the coefficient ring is algebraic over the real numbers, then the commutativity assumption, above, may be dropped.

References

Richard F. Arens and Irving Kaplansky, Topological representation of algebras, Trans. Amer. Math. Soc. 63 (1948), 457–481. MR 25453, DOI 10.1090/S0002-9947-1948-0025453-6

Eléments de mathématique

Algèbre commutative

Modules plats

Localisation

36

Andrew B. Carson, Representation of semi-simple algebraic algebras, J. Algebra 24 (1973), 245–257. MR 309931, DOI 10.1016/0021-8693(73)90136-1
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Anneaux cohérents

267

38

Un anneau cohérent dont l’anneau des polynômes n’est pas cohérent

267

38