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A module is called flat if taking the tensor product of it with any exact sequence of R-modules preserves exactness. Torsionless A module is called torsionless if it embeds into its algebraic dual. Simple A simple module S is a module that is not {0} and whose only submodules are {0} and S. Simple modules are sometimes called irreducible. [5 ...
Modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. [1] The concept of modularity is used primarily to reduce complexity by breaking a system into varying degrees of interdependence and independence across and "hide the complexity of each part behind an abstraction and interface". [2]
Modularity of mind is the notion that a mind may, at least in part, be composed of innate neural structures or mental modules which have distinct, established, and evolutionarily developed functions. However, different definitions of "module" have been proposed by different authors.
The mathematical model represents the physical model in virtual form, and conditions are applied that set up the experiment of interest. The simulation starts – i.e., the computer calculates the results of those conditions on the mathematical model – and outputs results in a format that is either machine- or human-readable, depending upon ...
Another model category is the category of chain complexes of R-modules for a commutative ring R. Homotopy theory in this context is homological algebra. Homology can then be viewed as a type of homotopy, allowing generalizations of homology to other objects, such as groups and R-algebras, one of the first major applications of the theory.
This page focuses on finitary first order model theory of infinite structures.. The relative emphasis placed on the class of models of a theory as opposed to the class of definable sets within a model fluctuated in the history of the subject, and the two directions are summarised by the pithy characterisations from 1973 and 1997 respectively:
The floating model rests on neither theory nor observation, but is merely the invocation of expected structure. Application of mathematics in social sciences outside of economics has been criticized for unfounded models. [5] Application of catastrophe theory in science has been characterized as a floating model. [6] Strategic vs. non-strategic.
In the V-Model, Unit Test Plans (UTPs) are developed during the module design phase. These UTPs are executed to eliminate bugs at the code level or unit level. A unit is the smallest entity that can independently exist, e.g. a program module.