ガロア第一論文と乗数イデアル他関連資料スレ3

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140: １３２人目の素数さん [] 2023/04/13(木) 17:37:57.11 ID:8Yc6OyrM

>>136
>>"regular"vs "zero divisor" の視点が記載されている
>　上記のregularの定義は？

お答えします
regularの定義は、下記のZero divisorの冒頭部分
”An element of a ring that is not a left zero divisor is called left regular or left cancellable.”
つまり、zero divisorの否定であって、”cancellable”なもの
”cancellable”は、文献[3]によるらしいが、それにはアクセスできない
なので想像だが
”cancellable”とは、乗法の逆元を持つことで、”cancel”可能と解釈したけど

https://en.wikipedia.org/wiki/Zero_divisor
Zero divisor

This is a partial case of divisibility in rings. An element that is a left or a right zero divisor is simply called a zero divisor.[2] An element a that is both a left and a right zero divisor is called a two-sided zero divisor (the nonzero x such that ax = 0 may be different from the nonzero y such that ya = 0). If the ring is commutative, then the left and right zero divisors are the same.

An element of a ring that is not a left zero divisor is called left regular or left cancellable.
Similarly, an element of a ring that is not a right zero divisor is called right regular or right cancellable. An element of a ring that is left and right cancellable, and is hence not a zero divisor, is called regular or cancellable,[3] or a non-zero-divisor. A zero divisor that is nonzero is called a nonzero zero divisor or a nontrivial zero divisor. A nonzero ring with no nontrivial zero divisors is called a domain.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1680684665/140

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