Hello, you have come here looking for the meaning of the word
minimal ideal. In DICTIOUS you will not only get to know all the dictionary meanings for the word
minimal ideal, but we will also tell you about its etymology, its characteristics and you will know how to say
minimal ideal in singular and plural. Everything you need to know about the word
minimal ideal you have here. The definition of the word
minimal ideal will help you to be more precise and correct when speaking or writing your texts. Knowing the definition of
minimal ideal, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.
English
Noun
minimal ideal (plural minimal ideals)
- (algebra, ring theory) A nonzero (two-sided) ideal that contains no other nonzero two-sided ideal.
1970, Mary W. Gray, A Radical Approach to Algebra, Addison-Wesley, page 33:Theorem 12. A semisimple ring R has only a finite number of minimal ideals and is their direct sum. Moreover, each minimal ideal is a simple ring.
2009, John Rhodes, Benjamin Steinberg, The q-theory of Finite Semigroups, Springer, page 596:Note that if a semigroup has a zero, then its minimal ideal is {0}. In this context, the notion of minimal ideal is not so useful, and so we introduce the notion of a 0-minimal ideal.
Coordinate terms
Further reading