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- Regular_ideal abstract "In mathematics, especially ring theory, a regular ideal can refer to multiple concepts.In operator theory, a right ideal in a (possibly) non-unital ring A is said to be regular (or modular) if there exists an element e in A such that for every . (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.A two-sided ideal of a ring R can also be called a (von Neumann) regular ideal if for each element x of there exists a y in such that xyx=x. (Goodearl 1991, p.2) (Kaplansky 1969, p.112)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. This article will use "quotient von Neumann regular" to refer to this type of regular ideal.Since the adjective regular has been overloaded, this article adopts the alternative adjectives modular, regular element von Neumann regular, and quotient von Neumann regular to distinguish between concepts.".
- Regular_ideal wikiPageID "24159446".
- Regular_ideal wikiPageRevisionID "603505014".
- Regular_ideal first "K.A.".
- Regular_ideal hasPhotoCollection Regular_ideal.
- Regular_ideal id "m/m064450.htm".
- Regular_ideal last "Zhevlakov".
- Regular_ideal title "Modular ideal".
- Regular_ideal subject Category:Ideals.
- Regular_ideal subject Category:Ring_theory.
- Regular_ideal type Abstraction100002137.
- Regular_ideal type Cognition100023271.
- Regular_ideal type Content105809192.
- Regular_ideal type Idea105833840.
- Regular_ideal type Ideal105923696.
- Regular_ideal type Ideals.
- Regular_ideal type PsychologicalFeature100023100.
- Regular_ideal comment "In mathematics, especially ring theory, a regular ideal can refer to multiple concepts.In operator theory, a right ideal in a (possibly) non-unital ring A is said to be regular (or modular) if there exists an element e in A such that for every . (Jacobson 1956)In commutative algebra a regular ideal refers to an ideal containing a non-zero divisor.".
- Regular_ideal label "Regular ideal".
- Regular_ideal sameAs m.07kg0l0.
- Regular_ideal sameAs Q7309603.
- Regular_ideal sameAs Q7309603.
- Regular_ideal sameAs Regular_ideal.
- Regular_ideal wasDerivedFrom Regular_ideal?oldid=603505014.
- Regular_ideal isPrimaryTopicOf Regular_ideal.