Some applications of Gr¨obner bases in homological algebra (São Paulo Journal of Mathematical Sciences, 2009)
In this paper we make some computations in homological algebra using Gr¨obner bases for modules over polynomials rings with coefficients in a Noetherian commutative ring. In particular, we show easy procedures for computing the Ext and Tor modules.Key words and phrases: Gr¨obner bases, syzygies, finite presentation of a module, free resolutions, Ext, Tor. 2000 Mathematics Subject Classification: Primary: 13P10. Secondary: 13D02, 13D07.