Primal ideal
Encyclopedia
In mathematics
, an element a of a commutative ring
A is called (relatively) prime to an ideal Q if whenever ab is an element of Q then b is also an element of Q.
A proper ideal
Q of a commutative ring
A is said to be primal if the elements that are not prime to it form an ideal.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, an element a of a commutative ring
Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra....
A is called (relatively) prime to an ideal Q if whenever ab is an element of Q then b is also an element of Q.
A proper ideal
Ideal (ring theory)
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept allows the generalization in an appropriate way of some important properties of integers like "even number" or "multiple of 3"....
Q of a commutative ring
Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra....
A is said to be primal if the elements that are not prime to it form an ideal.