Regular ideal

In mathematics, especially ring theory, a regular ideal can refer to multiple concepts.

In operator theory, a right ideal ${\displaystyle {\mathfrak {i}}}$ in a (possibly) non-unital ring A is said to be regular (or modular) if there exists an element e in A such that ${\displaystyle ex-x\in {\mathfrak {i}}}$ for every ${\displaystyle x\in A}$. (Jacobson 1956)

In commutative algebra a regular ideal refers to an ideal containing a non-zero divisor. (Larsen & McCarthy 1971, p.42) This article will use "regular element ideal" to help distinguish this type of ideal.

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