## Huishi Li

*On computation of minimal free resolutions over solvable polynomial algebras*

Comment.Math.Univ.Carolin. 56,4 (2015) 447-503.**Abstract:**Let $A=K[a_1,\ldots ,a_n]$ be a (noncommutative) solvable polynomial algebra over a field $K$ in the sense of A.~Kandri-Rody and V.~Weispfenning [{\it Non-commutative Gr\"obner bases in algebras of solvable type\/}, J. Symbolic Comput. {\bf 9} (1990), 1--26]. This paper presents a comprehensive study on the computation of minimal free resolutions of modules over $A$ in the following two cases: (1) $A=\bigoplus_{p\in\mathbb{N}}A_p$ is an $\mathbb{N}$-graded algebra with the degree-0 homogeneous part $A_0=K$; (2) $A$ is an $\mathbb{N}$-filtered algebra with the filtration $\{F_pA\}_{p\in\mathbb{N}}$ determined by a~ positive-degree function on $A$.

**Keywords:** solvable polynomial algebra; Gr\"obner basis; minimal free resolution

**DOI:** DOI 10.14712/1213-7243.2015.141

**AMS Subject Classification:** 16W70 16Z05

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