单词 | zero divisor |
释义 | BETA Examples ofzero divisorDictionary> Examples ofzero divisor zero divisorisn’t in the Cambridge Dictionary yet. You can help! Add a definition Similarly, an element of a ring is called a rightzerodivisorif there exists a nonzero such that. From Wikipedia ![]() An element that is a left or a rightzerodivisoris simply called azerodivisor. From Wikipedia ![]() A weaker notion of being bad, weaker than being azerodivisor, is being a non-unit (not invertible under multiplication). From Wikipedia ![]() The conjecture remains open in full generality, however some special cases of torsion-free groups have been shown to satisfy thezerodivisorconjecture. From Wikipedia ![]() The converse does not hold: an element which is not azerodivisoris not guaranteed to have a multiplicative inverse. From Wikipedia ![]() An element of a ring that is not azerodivisoris called regular, or a non-zero-divisor. From Wikipedia ![]() Any non-trivial idempotent "a" is azerodivisor(because with neither "a" nor "b" being zero, where). From Wikipedia ![]() A rightzerodivisoris defined similarly. From Wikipedia ![]() The naive solution is to replace the fraction field by the total quotient ring, that is, to invert every element that is not azerodivisor. From Wikipedia ![]() An element that is both a left and a rightzerodivisoris called a two-sidedzerodivisor(the nonzero such that may be different from the nonzero such that). From Wikipedia ![]() A torsion-free module is a module over a ring such that 0 is the only element annihilated by a regular element (nonzero-divisor) of the ring. From Wikipedia ![]() 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 ![]() That is, it is a ring which has no left or right zero divisors. From Wikipedia ![]() The zero-product property is also known as the rule of zero product or nonexistence of nontrivial zero divisors. From Wikipedia ![]() Indeed, they are (trivially) zero divisors and clearly form an ideal of the associative algebra (and thus ring) of the dual numbers. From Wikipedia ![]() 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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