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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.
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.
An introduction to persistent identifiers and FAIR data.. A persistent identifier (PI or PID) is a long-lasting reference to a document, file, web page, or other object.. The term "persistent identifier" is usually used in the context of digital objects that are accessible over the Internet.
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