Integral domain: Difference between revisions
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* {{cite book | author= Iain T. Adamson | title=Elementary rings and modules | series=University Mathematical Texts | publisher=Oliver and Boyd | year=1972 | isbn=0-05-002192-3 }} | * {{cite book | author= Iain T. Adamson | title=Elementary rings and modules | series=University Mathematical Texts | publisher=Oliver and Boyd | year=1972 | isbn=0-05-002192-3 }} | ||
* {{cite book | author=David Sharpe | title=Rings and factorization | publisher=[[Cambridge University Press]] | year=1987 | isbn=0-521-33718-6 }} | * {{cite book | author=David Sharpe | title=Rings and factorization | publisher=[[Cambridge University Press]] | year=1987 | isbn=0-521-33718-6 }}[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 17:00, 1 September 2024
In ring theory, an integral domain is a commutative ring in which there are no non-trivial zero divisors: that is the product of non-zero elements is again non-zero. The term entire ring is sometimes used.[1]
Properties
- A commutative ring is an integral domain if and only if the zero ideal is prime.
- A ring is an integral domain if and only if it is isomorphic to a subring of a field.
References
- ↑ Serge Lang (1993). Algebra, 3rd ed.. Addison-Wesley, 91-92. ISBN 0-201-55540-9.
- Iain T. Adamson (1972). Elementary rings and modules. Oliver and Boyd. ISBN 0-05-002192-3.
- David Sharpe (1987). Rings and factorization. Cambridge University Press. ISBN 0-521-33718-6.