Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1335-3765-1 |
Объём: | 96 страниц |
Масса: | 166 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
High Quality Content by WIKIPEDIA articles! In abstract algebra, a principal ideal domain, or PID is an integral domain in which every ideal is principal, i.e., can be generated by a single element. More generally, a principal ideal ring is a nonzero commutative ring whose ideals are principal, although some authors (e.g., Bourbaki) refer to PIDs as principal rings. The distinction is that a principal ideal ring may have zero divisors whereas a principal ideal domain cannot. Principal ideal domains are thus mathematical objects which behave somewhat like the integers, with respect to divisibility: any element of a PID has a unique decomposition into prime elements (so an analogue of the fundamental theorem of arithmetic holds); any two elements of a PID have a greatest common divisor (although it may not be possible to find it using the Euclidean algorithm). If x and y are elements of a PID without common divisors, then every element of the PID can be written in the form ax + by.
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