Marot Ring
In mathematics, a Marot ring, introduced by , is a commutative ring whose regular ideal In mathematics, especially ring theory, a regular ideal can refer to multiple concepts. In operator theory, a right ideal (ring theory), ideal \mathfrak in a (possibly) non-unital ring ''A'' is said to be regular (or modular) if there exists an ele ...s are generated by regular elements. References Ring theory {{abstract-algebra-stub ...
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Regular Ideal
In mathematics, especially ring theory, a regular ideal can refer to multiple concepts. In operator theory, a right ideal (ring theory), ideal \mathfrak in a (possibly) non-unital ring ''A'' is said to be regular (or modular) if there exists an element ''e'' in ''A'' such that ex - x \in \mathfrak for every x \in A. In commutative algebra a regular ideal refers to an ideal containing a non-zero divisor. This article will use "regular element ideal" to help distinguish this type of ideal. A two-sided ideal \mathfrak of a ring ''R'' can also be called a (von Neumann) regular ideal if for each element ''x'' of \mathfrak there exists a ''y'' in \mathfrak such that ''xyx''=''x''. Finally, regular ideal has been used to refer to an ideal ''J'' of a ring ''R'' such that the quotient ring ''R''/''J'' is von Neumann regular ring.Burton, D.M. (1970) ''A first course in rings and ideals.'' Addison-Wesley. Reading, Massachusetts . This article will use "quotient von Neumann regular" to refer ...
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