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Group-like Small Cancellation Theory for Ringsстатья
- Авторы: Atkarskaya A., Kanel-Belov A., Plotkin E., Rips E.
- Журнал: International Journal of Algebra and Computation
- Год издания: 2023
- Издательство: World Scientific Publishing Co
- Местоположение издательства: Singapore
- DOI: 10.1142/s0218196723500522
- Аннотация: n the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding defining relations. We show that the obtained ring is non-trivial. Moreover, we show that this ring enjoys a global filtration that agrees with relations, find a basis of the ring as a vector space and establish the corresponding structure theorems. We also provide a revision of a concept of Gröbner basis for our rings and establish a greedy algorithm for the Ideal Membership Problem
- Добавил в систему: Белов Алексей Яковлевич