Deformations of a two-generator purely inseparable field of exponent $1$
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- by Francis P. Callahan PDF
- Proc. Amer. Math. Soc. 62 (1977), 189-195 Request permission
Abstract:
This paper gives a discussion of the algebraic deformations of a two-generator purely inseparable field of exponent 1, this being the simplest field having noncommutative deformations. It gives a necessary condition for a 2-cocycle to be integrable and, if it is allowed to adjoin a single separable element to the groundfield, also a sufficient condition for a 2-cocycle to be integrable. The method used is to study certain skew symmetric biderivations associated with the field.References
- Murray Gerstenhaber, On the deformation of rings and algebras, Ann. of Math. (2) 79 (1964), 59–103. MR 171807, DOI 10.2307/1970484
- Nathan Jacobson, Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. MR 0172871
- F. P. Callahan, An identity satisfied by derivations of a purely inseparable field, Amer. Math. Monthly 80 (1973), 40–42. MR 450248, DOI 10.2307/2319256
- G. Hochschild, On the cohomology groups of an associative algebra, Ann. of Math. (2) 46 (1945), 58–67. MR 11076, DOI 10.2307/1969145
- Murray Gerstenhaber, On the deformation of rings and algebras. III, Ann. of Math. (2) 88 (1968), 1–34. MR 240167, DOI 10.2307/1970553
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 189-195
- MSC: Primary 12F15
- DOI: https://doi.org/10.1090/S0002-9939-1977-0568489-2
- MathSciNet review: 0568489