4 articles
Global dimension
Global dimension, also called global homological dimension, is the supremum of the projective dimensions of modules over a ring, measuring how far the ring is from semisimple.
Injective module
An injective module is a module J over a ring R such that every homomorphism from a submodule into J extends to the whole module, the dual of projectivity.
Projective module
A projective module, also called a finitely generated projective module in the finite case, is a module over a ring that behaves like a free module, characterized by the lifting property for homomorphisms.
Regular local ring
A regular local ring is a commutative Noetherian local ring whose maximal ideal can be generated by as many elements as its Krull dimension, making it algebraically smooth.