Study of a division-like property

Pub Date : 2024-04-01 DOI:10.1142/s0219498825502214
Robin Khanfir, Béranger Seguin
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Abstract

We study a weak divisibility property for noncommutative rings: A nontrivial ring is fadelian if for all nonzero a and x there exist b,c such that x=ab+ca. We prove properties of fadelian rings and construct examples thereof which are not division rings, as well as non-Noetherian and non-Ore examples.

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类似除法性质的研究
我们研究非交换环的弱可分性:如果对于所有非零的 a 和 x,存在 b、c,使得 x=ab+ca ,那么一个非琐环就是法德环。我们证明了非可分割环的性质,并构造了非可分割环的例子,以及非诺特环和非奥尔环的例子。
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