Explore: Free Resolutions (algebra)

to be free). Thus one speaks of a P resolution. In particular, every module has free resolutions, projective resolutions and flat resolutions, which

semi-simplicity. The fourth part, Homological Algebra, covers general homology theory and finite free resolutions. The Mathematical Association of America

the bar resolution, bar construction, standard resolution, or standard complex, is a way of constructing resolutions in homological algebra. It was first

Standard resolution, the bar construction of resolutions in homological algebra Resolution of singularities in algebraic geometry Resolution (audio),

In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over

In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over

Macaulay2 is a free computer algebra system created by Daniel Grayson (from the University of Illinois at Urbana–Champaign) and Michael Stillman (from

In homological algebra, a branch of mathematics, a matrix factorization is a tool used to study infinitely long resolutions, generally over commutative

of the ground field. There are Koszul algebras whose ground fields have infinite minimal graded free resolutions, e.g, R = k [ x , y ] / ( x y ) {\displaystyle

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins