noun
Meaning 1
Given a commutative unital ring R with extension ring S (i.e., that is a subring of S), any element s ∈ S that is a root of some monic polynomial with coefficients in R.
Definition source: English Wiktionary via Wiktextract
Qualifier: commutative algebra; ring theory; commutative algebra; ring theory
Topics: algebra, mathematics, sciences
Examples
- 1956, Unnamed translator, D. K Faddeev, Simple Algebras Over a Field of Algebraic Functions of One Variable, in Five Papers on Logic Algebra, and Number Theory, American Mathematical Society Translations, Series 2, Volume 3, page 21, A subring of B containing the ring o of integral elements of the field k_0(π), distinct from B, and not contained in any other subring of B distinct from B, is called a maximal ring of the algebra B. In a division algebra, the only maximal ring is the ring of integral elements.
- 1970 [Frederick Ungar Publishing], John R. Schulenberger (translator), B. L. van der Waerden, Algebra, Volume 2, 1991, Springer, 2003 Softcover Reprint, page 172, If S is the ring of integral elements in a commutative ring T (over a subring R) and if the element t of T is integral over S, then t is also integral over R (that is, contained in S).
Meaning relationships
Synonyms: none provided
Antonyms: none provided