Properties of free Baxter algebras. (English) Zbl 0964.16028
In a previous paper [ibid. 151, No. 1, 101-127 (2000); see the preceding review Zbl 0964.16027], the author and W. Keigher gave two descriptions of a free Baxter algebra, which they called a shuffle Baxter algebra and a standard Baxter algebra. In the paper under review, the author notes that this algebra is not always an integral domain and is not always reduced. Obstructions to these properties include the characteristic, the weight of the Baxter algebra, whether or not there is an identity element and whether or not it is complete. He gives necessary and sufficient conditions for a free Baxter algebra to be an integral domain or to be reduced. When it is not reduced, he describes the nilpotent radical.
Reviewer: Earl J.Taft (New Brunswick)
MSC:
| 16S10 | Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) |
| 05A19 | Combinatorial identities, bijective combinatorics |
| 16W35 | Ring-theoretic aspects of quantum groups (MSC2000) |
Keywords:
free Baxter algebras; shuffle Baxter algebras; standard Baxter algebras; nilpotent radicalsCitations:
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