| 词汇 | zero-divisor |
| 释义 | BETA zero divisorcollocation in Englishmeanings of zeroand divisorThese words are often used together. Click on the links below to explore the meanings. zero adjective uk /ˈzɪə.rəʊ/ us /ˈzɪr.oʊ/ nothing or 0 ... See more at zero divisor noun[ C ] uk /dɪˈvaɪ.zər/ us /dɪˈvaɪ.zɚ/ a number by which another number is divided in ... See more at divisor Examples of zero divisorzero divisor Similarly, an element of a ring is called a right zerodivisor if there exists a nonzero such that. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. An element that is a left or a right zerodivisor is simply called a zerodivisor. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A weaker notion of being bad, weaker than being a zerodivisor, is being a non-unit (not invertible under multiplication). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The conjecture remains open in full generality, however some special cases of torsion-free groups have been shown to satisfy the zerodivisor conjecture. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The converse does not hold: an element which is not a zerodivisor is not guaranteed to have a multiplicative inverse. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. An element of a ring that is not a zerodivisor is called regular, or a non-zero-divisor. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Any non-trivial idempotent "a" is a zerodivisor (because with neither "a" nor "b" being zero, where). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A right zerodivisor is defined similarly. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The naive solution is to replace the fraction field by the total quotient ring, that is, to invert every element that is not a zerodivisor. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. An element that is both a left and a right zerodivisor is called a two-sided zerodivisor (the nonzero such that may be different from the nonzero such that). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A torsion-free module is a module over a ring such that 0 is the only element annihilated by a regular element (non zero-divisor) of the ring. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. If the ring or algebra is finite, however, then all elements "a" which are not zero divisors do have a (left and right) inverse. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. That is, it is a ring which has no left or right zero divisors. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The zero-product property is also known as the rule of zero product or nonexistence of nontrivial zero divisors. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Indeed, they are (trivially) zero divisors and clearly form an ideal of the associative algebra (and thus ring) of the dual numbers. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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