Search results
Results From The WOW.Com Content Network
The intersection of all subrings of a ring R is a subring that may be called the prime subring of R by analogy with prime fields. The prime subring of a ring R is a subring of the center of R , which is isomorphic either to the ring Z {\displaystyle \mathbb {Z} } of the integers or to the ring of the integers modulo n , where n is the smallest ...
In computer programming, bounds checking is any method of detecting whether a variable is within some bounds before it is used. It is usually used to ensure that a number fits into a given type (range checking), or that a variable being used as an array index is within the bounds of the array (index checking).
An intersection of subrings is a subring. Given a subset E of R, the smallest subring of R containing E is the intersection of all subrings of R containing E, and it is called the subring generated by E. For a ring R, the smallest subring of R is called the characteristic subring of R. It can be generated through addition of copies of 1 and −1.
The C language specification includes the typedef s size_t and ptrdiff_t to represent memory-related quantities. Their size is defined according to the target processor's arithmetic capabilities, not the memory capabilities, such as available address space. Both of these types are defined in the <stddef.h> header (cstddef in C++).
For example, [] is the smallest subring of C containing all the integers and ; it consists of all numbers of the form +, where m and n are arbitrary integers. Another example: Z [ 1 / 2 ] {\displaystyle \mathbf {Z} [1/2]} is the subring of Q consisting of all rational numbers whose denominator is a power of 2 .
A memory address a is said to be n-byte aligned when a is a multiple of n (where n is a power of 2). In this context, a byte is the smallest unit of memory access, i.e. each memory address specifies a different byte.
The Gaussian integers are the set [1] [] = {+,}, =In other words, a Gaussian integer is a complex number such that its real and imaginary parts are both integers.Since the Gaussian integers are closed under addition and multiplication, they form a commutative ring, which is a subring of the field of complex numbers.
Likewise, any subring of a Boolean ring is a Boolean ring. Any localization RS −1 of a Boolean ring R by a set S ⊆ R is a Boolean ring, since every element in the localization is idempotent. The maximal ring of quotients Q(R) (in the sense of Utumi and Lambek) of a Boolean ring R is a Boolean ring, since every partial endomorphism is ...