primitive ideal is the annihilator of a (nonzero) simple left module. A right primitive ideal is defined similarly. Left and right primitive ideals are...

number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime. An ideal P of a commutative ring R is...

element. Finitely generated ideal: This type of ideal is finitely generated as a module. Primitive ideal: A left primitive ideal is the annihilator of a simple...

left primitive rings is as follows: a ring is left primitive if and only if there is a maximal left ideal containing no nonzero two-sided ideals. The...

in terms of the primitive spectrum . The primitive spectrum of A is the set of primitive ideals Prim(A) of A, where a primitive ideal is the kernel of...

that every prime ideal is an intersection of primitive ideals. For commutative rings primitive ideals are the same as maximal ideals so in this case a...

annihilators of simple left modules. An ideal that is the annihilator of a simple module is known as a primitive ideal, and so a reformulation of this states...

unique factorization of ideals. In particular, many Z [ ζ p ] , {\displaystyle \mathbb {Z} [\zeta _{p}],} for the primitive p-th root of unity ζ p ,...

architecture. The idea of The Primitive Hut contends that the ideal architectural form embodies what is natural and intrinsic. The Primitive Hut as an architectural...

particular, the dual of a locally compact group is defined to be the primitive ideal space of the group C*-algebra. See spectrum of a C*-algebra. Von Neumann...