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.
Finitely generated moduleIn mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over R, or a module of finite type. Related concepts include finitely cogenerated modules, finitely presented modules, finitely related modules and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.
Economic sectorOne classical breakdown of economic activity distinguishes three sectors: Primary: involves the retrieval and production of raw-material commodities, such as corn, coal, wood or iron. Miners, farmers and fishermen are all workers in the primary sector. Secondary: involves the transformation of raw or intermediate materials into goods, as in steel into cars, or textiles into clothing. Builders and dressmakers work in the secondary sector. Tertiary: involves the supplying of services to consumers and businesses, such as babysitting, cinemas or banking.
Private sectorThe private sector is the part of the economy, sometimes referred to as the citizen sector, which is owned by private groups, usually as a means of establishment for profit or non profit, rather than being owned by the government. The private sector employs most of the workforce in some countries. In private sector, activities are guided by the motive to earn money. A 2013 study by the International Finance Corporation (part of the World Bank Group) identified that 90 percent of jobs in developing countries are in the private sector.
Three-sector modelThe three-sector model in economics divides economies into three sectors of activity: extraction of raw materials (primary), manufacturing (secondary), and service industries which exist to facilitate the transport, distribution and sale of goods produced in the secondary sector (tertiary). The model was developed by Allan Fisher, Colin Clark, and Jean Fourastié in the first half of the 20th century, and is a representation of an industrial economy. It has been criticised as inappropriate as a representation of the economy in the 21st century.
Tertiary sector of the economyThe tertiary sector of the economy, generally known as the service sector, is the third of the three economic sectors in the three-sector model (also known as the economic cycle). The others are the primary sector (raw materials) and the secondary sector (manufacturing). The tertiary sector consists of the provision of services instead of end products. Services (also known as "intangible goods") include attention, advice, access, experience and affective labour.
Primary sector of the economyThe primary sector of the economy includes any industry involved in the extraction and production of raw materials, such as farming, logging, fishing, forestry and mining. The primary sector tends to make up a larger portion of the economy in developing countries than it does in developed countries. For example, in 2018, agriculture, forestry, and fishing comprised more than 15% of GDP in sub-Saharan Africa but less than 1% of GDP in North America.
