|
This article is cited in 1 scientific paper (total in 1 paper)
On Some Algorithmic Problems Related to Varieties of Nonassociative Rings
V. Yu. Popov Ural State Technical University
Abstract:
It is proven that there exists no algorithm deciding whether the variety $\mathrm{var}\Sigma$ is finitely based relative to an arbitrary recursive system of ring identities $\Sigma$. An infinite sequence is constructed of finitely based varieties of nonassociative rings $\mathfrak A_1\supset\mathfrak B_1\supset\mathfrak A_2\supset\mathfrak B_2 \supset\dotsb$ such that, for all $i$, the equational theory of $\mathfrak A_i$ is undecidable and the equational theory of $\mathfrak B_i$ is decidable.
Key words:
variety of rings, finitely based variety, equational theory, decidable theory, undecidable theory.
Received: 27.10.1999
Citation:
V. Yu. Popov, “On Some Algorithmic Problems Related to Varieties of Nonassociative Rings”, Mat. Tr., 3:2 (2000), 146–170; Siberian Adv. Math., 11:2 (2001), 60–82
Linking options:
https://www.mathnet.ru/eng/mt170 https://www.mathnet.ru/eng/mt/v3/i2/p146
|
Statistics & downloads: |
Abstract page: | 165 | Full-text PDF : | 75 | First page: | 1 |
|