Resolution
Resolution is a widely used word with many different meanings. It can refer to resolution of equations, resolution ofsingularities (in Algebraic Geometry), resolution of modules or more sophisticated structures, etc. In a BlockDesign, a Partition 
of a BIBD's set of blocks 
into Parallel Classes, each of whichin turn partitions the set 
, is called a resolution (Abel and Furino 1996).
A resolution of the Module 
over the Ring is a complex of -modules 
and morphisms 
and aMorphism 
such that
satisfying the following conditions:
- 1. The composition of any two consecutive morphisms is the zero map,
- 2. For all
, 
, - 3.
,
is the
th Homology Group.If all modules are projective (free), then the resolution is called projective (free). There is a similar concept forresolutions ``to the right'' of , which are called injective resolutions.
References
Abel, R. J. R. and Furino, S. C. ``Resolvable and Near Resolvable Designs.'' §I.6 in The CRC Handbook of Combinatorial Designs (Ed. C. J. Colbourn and J. H. Dinitz). Boca Raton, FL: CRC Press, pp. 4 and 87-94, 1996. Jacobson, N. Basic Algebra II, 2nd ed. New York: W. H. Freeman, p. 339, 1989.