2 4 A pr 2 00 4 Ascending Chain Conditions in Free Baxter Algebras ∗
نویسنده
چکیده
In this paper we study ascending chain conditions in a free Baxter algebra by making use of explicit constructions of free Baxter algebras that were obtained recently. We investigate ascending chain conditions both for ideals and for Baxter ideals. The free Baxter algebras under consideration include free Baxter algebras on sets and free Baxter algebras on algebras. We also consider complete free Baxter algebras.
منابع مشابه
J ul 2 00 4 Properties of Free Baxter Algebras ∗
The study of free Baxter algebras was started by Rota and Cartier thirty years ago. We continue this study by applying two recent constructions of free Baxter algebras. We investigate the basic structure of a free Baxter algebra, and characterize in detail when a free Baxter algebra is a domain or a reduced algebra. We also describe the nilpotent radical of a free Baxter algebra when it is not ...
متن کاملm at h . R A ] 1 4 O ct 2 00 5 ON FREE ROTA – BAXTER ALGEBRAS
Most of the studies on Rota–Baxter algebras (also known as Baxter algebras) have been for commutative algebras. Free commutative Rota–Baxter algebras were constructed by Rota and Cartier in the 1970s. A later construction was obtained by Keigher and one of the authors in terms of mixable shuffles. Recently, noncommutative Rota–Baxter algebras have appeared both in physics in connection with the...
متن کامل2 00 5 Rota - Baxter Algebras , Dendriform Algebras and Poincaré - Birkhoff - Witt Theorem
Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double shuffle relations for multiple zeta values. The interest in the non-commutative setting arose in connection with the work of Connes and Kreimer on th...
متن کاملM ar 2 00 5 ROTA - BAXTER ALGEBRAS , DENDRIFORM ALGEBRAS AND POINCARÉ - BIRKHOFF - WITT THEOREM
Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double shuffle relations for multiple zeta values. The interest in the non-commutative setting arised in connection with the work of Connes and Kreimer on t...
متن کامل. R A ] 1 3 O ct 2 00 5 ON FREE ROTA – BAXTER ALGEBRAS
Most of the studies on Rota–Baxter algebras (also known as Baxter algebras) have been for commutative algebras. Free commutative Rota–Baxter algebras were constructed by Rota and Cartier in the 1970s. A later construction was obtained by Keigher and one of the authors in terms of mixable shuffles. Recently, noncommutative Rota–Baxter algebras have appeared both in physics in connection with the...
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