Content (algebra): Difference between revisions
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In [[algebra]], the '''content''' of a [[polynomial]] is the [[highest common factor]] of its coefficients. | In [[algebra]], the '''content''' of a [[polynomial]] is the [[highest common factor]] of its coefficients. | ||
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* {{cite book | author=B. Hartley | authorlink=Brian Hartley | coauthors=T.O. Hawkes | title=Rings, modules and linear algebra | publisher=Chapman and Hall | year=1970 | isbn=0-412-09810-5 }} | * {{cite book | author=B. Hartley | authorlink=Brian Hartley | coauthors=T.O. Hawkes | title=Rings, modules and linear algebra | publisher=Chapman and Hall | year=1970 | isbn=0-412-09810-5 }} | ||
* {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55540-9 | page=181 }} | * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55540-9 | page=181 }} | ||
* {{cite book | author=David Sharpe | title=Rings and factorization | publisher=[[Cambridge University Press]] | year=1987 | isbn=0-521-33718-6 | pages=68-69 }} | * {{cite book | author=David Sharpe | title=Rings and factorization | publisher=[[Cambridge University Press]] | year=1987 | isbn=0-521-33718-6 | pages=68-69 }}[[Category:Suggestion Bot Tag]] | ||
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Latest revision as of 16:00, 1 August 2024
In algebra, the content of a polynomial is the highest common factor of its coefficients.
A polynomial is primitive if it has content unity.
Gauss's lemma for polynomials may be expressed as stating that for polynomials over a unique factorization domain, the content of the product of two polynomials is the product of their contents.
References
- B. Hartley; T.O. Hawkes (1970). Rings, modules and linear algebra. Chapman and Hall. ISBN 0-412-09810-5.
- Serge Lang (1993). Algebra, 3rd ed.. Addison-Wesley. ISBN 0-201-55540-9.
- David Sharpe (1987). Rings and factorization. Cambridge University Press, 68-69. ISBN 0-521-33718-6.