Problems in algebra inspired by universal algebraic geometry
| dc.creator | Plotkin, Boris | |
| dc.date | 2004-06-06 | |
| dc.date | 2004-12-14 | |
| dc.date.accessioned | 2026-07-07T05:08:55Z | |
| dc.date.available | 2026-07-07T05:08:55Z | |
| dc.description | Let $Θ$ be a variety of algebras. In every $Θ$ and every algebra $H$ from $Θ$ one can consider algebraic geometry in $Θ$ over $H$. We consider also a special categorical invariant $K_Θ(H)$ of this geometry. The classical algebraic geometry deals with the variety $Θ=Com-P$ of all associative and commutative algebras over the ground field of constants $P$. An algebra $H$ in this setting is an extension of the ground field $P$. Geometry in groups is related to varieties $\Grp$ and $\Grp-G$, where $G$ is a group of constants. The case $\Grp -F$ where $F$ is a free group, is related to Tarski's problems devoted to logic of a free group. he described general insight on algebraic geometry in different varieties of algebras inspires some new problems in algebra and algebraic geometry. The problems of such kind determine, to a great extent, the content of universal algebraic geometry. We start with the short overview of main definitions and results and then consider the list of unsolved problems. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406101 | |
| dc.identifier | http://arxiv.org/abs/math/0406101 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71449 | |
| dc.subject | General Mathematics | |
| dc.subject | 03C05;03G99;16B70;08A70 | |
| dc.title | Problems in algebra inspired by universal algebraic geometry | |
| dc.type | text |