Module (mathematics)In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers. Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operation of addition between elements of the ring or module and is compatible with the ring multiplication.
Voluntary sectorThe voluntary sector, independent sector, or civic sector is the realm of social activity undertaken by organizations that are non-governmental nonprofit organizations. This sector is also called the third sector, community sector, and nonprofit sector, in contrast to the public sector and the private sector. Civic sector or social sector are other terms for the sector, emphasizing its relationship to civil society. Richard Cornuelle coined the term "independent sector" and was one of the first scholars to point out the vast impact and unique mechanisms of this sector.
Free moduleIn mathematics, a free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Every vector space is a free module, but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. Given any set S and ring R, there is a free R-module with basis S, which is called the free module on S or module of formal R-linear combinations of the elements of S. A free abelian group is precisely a free module over the ring Z of integers.
Public sectorThe public sector, also called the state sector, is the part of the economy composed of both public services and public enterprises. Public sectors include the public goods and governmental services such as the military, law enforcement, infrastructure, public transit, public education, along with health care and those working for the government itself, such as elected officials. The public sector might provide services that a non-payer cannot be excluded from (such as street lighting), services which benefit all of society rather than just the individual who uses the service.
Projective moduleIn mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizations of these modules appear below. Every free module is a projective module, but the converse fails to hold over some rings, such as Dedekind rings that are not principal ideal domains.
