Showing papers on "Free algebra published in 1978"
04 Sep 1978
52 citations
16 citations
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TL;DR: In this paper, the universal ring decomposition theorem of affine commutative free groups has been shown to hold even when X is a monoid-scheme over a perfect field k of positive caracteristic.
Abstract: Let X=Sp A be an affine scheme over a perfect field k of positive caracteristic. The functor D(k)-mod (W(A), (w(?)) is the unipotent part of the affine commutative free group generated by X (W is the ring of Witt-vectors and D the ring of Dieudonne). If X is a monoid-scheme, this free group has a structure of ring scheme. In particular, if X=0kx, we obtain a new proof of the theorem of decomposition of the universal ring.
TL;DR: In this article, the authors give a short combinatorial proof (independent of Schdtzenberger's result) of the following: let X* + T be a homomorphism ont0 the monoid T with
Abstract: some positive integer and Y is a subset of X. This result is an easy consequence of a fundamental result of M. P. Schdtzenberger [I], viz: If C is a finite code for which syn(C*) is a group or a group with zero then C = yk for some Y c X and some integer k. In this note we give a short combinatorial proof (independent of Sch~tzenberger's result) of the following: let ~:X* + T be a homomorphism ont0 the monoid T with