Search results
Results from the WOW.Com Content Network
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 ...
With modular programming, concerns are separated such that modules perform logically discrete functions, interacting through well-defined interfaces. Often modules form a directed acyclic graph (DAG); in this case a cyclic dependency between modules is seen as indicating that these should be a single module. In the case where modules do form a ...
A modular function is a function that is invariant with respect to the modular group, but without the condition that it be holomorphic in the upper half-plane (among other requirements). Instead, modular functions are meromorphic: they are holomorphic on the complement of a set of isolated points, which are poles of the function.
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]
The dual module of a module M over a commutative ring R is the module (,). dualizing dualizing module Drinfeld A Drinfeld module is a module over a ring of functions on algebraic curve with coefficients from a finite field.
With a direct product, some natural group homomorphisms are obtained for free: the projection maps defined by :, (,) =:, (,) = are called the coordinate functions. Also, every homomorphism f {\displaystyle f} to the direct product is totally determined by its component functions f i = π i ∘ f . {\displaystyle f_{i}=\pi _{i}\circ f.}
Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
A built-in function, or builtin function, or intrinsic function, is a function for which the compiler generates code at compile time or provides in a way other than for other functions. [23] A built-in function does not need to be defined like other functions since it is built in to the programming language. [24]