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An assessor's parcel number, or APN, is a number assigned to parcels of real property by the tax assessor of a particular jurisdiction for purposes of identification and record-keeping. The assigned number is unique within the particular jurisdiction, and may conform to certain formatting standards that convey basic identifying information such ...
In mathematics, a principal ideal domain, or PID, is an integral domain (that is, a commutative ring without nonzero zero divisors) in which every ideal is principal (that is, is formed by the multiples of a single element). Some authors such as Bourbaki refer to PIDs as principal rings.
In computing, the process identifier (a.k.a. process ID or PID) is a number used by most operating system kernels—such as those of Unix, macOS and Windows—to uniquely identify an active process. This number may be used as a parameter in various function calls, allowing processes to be manipulated, such as adjusting the process's priority or ...
In practice, (2) and (3) are the most useful conditions to check. For example, it follows immediately from (2) that a PID is a UFD, since every prime ideal is generated by a prime element in a PID. For another example, consider a Noetherian integral domain in which every height one prime ideal is principal.
The ring = of algebraic integers in a number field K is Noetherian, integrally closed, and of dimension one: to see the last property, observe that for any nonzero prime ideal I of R, R/I is a finite set, and recall that a finite integral domain is a field; so by (DD4) R is a Dedekind domain. As above, this includes all the examples considered ...
This strange property can be used to show that some principal ideal domains are not Euclidean domains, as not all PIDs have this property. For example, for d = −19, −43, −67, −163, the ring of integers of () is a PID which is not Euclidean, but the cases d = −1, −2, −3, −7, −11 are Euclidean.
PID controller (proportional-integral-derivative controller), a control concept used in automation; Piping and instrumentation diagram (P&ID), a diagram in the process industry which shows the piping of the process flow etc. Principal ideal domain, an algebraic structure; Process identifier, a number used by many operating systems to identify a ...
Each of the listed programs is identified by a 16-bit value called program_number. Each of the programs listed in PAT has an associated value of PID for its PMT. The value 0x0000 for program_number is reserved to specify the PID where to look for network information table. If such a program is not present in PAT the default PID value (0x0010 ...