In ring theory, a branch of mathematics, semiprime ideals and semiprime rings are generalizations of prime ideals and prime rings. In commutative algebra...

I of a ring R is semiprime if for any ideal A of R, An ⊆ I implies A ⊆ I. Equivalently, I is semiprime if and only if R/I is a semiprime ring. semiprimitive...

generalized to non-commutative rings in the semiprime ring article. The radical of an ideal I {\displaystyle I} in a commutative ring R {\displaystyle R} , denoted...

or semiprime if for any a in R {\displaystyle R} , if an is in I for some n, then a is in I. The factor ring of a radical ideal is a semiprime ring for...

ideals are prime, and prime ideals are both primary and semiprime. An ideal P of a commutative ring R is prime if it has the following two properties: If...

the semiprime right Goldie rings are precisely those that have a semisimple Artinian right classical ring of quotients. The structure of this ring of quotients...

determines the structure of primitive rings Goldie's theorem determines the structure of semiprime Goldie rings The Zariski–Samuel theorem determines...

the semiprime right Goldie rings are precisely those that have a semisimple Artinian right classical ring of quotients. The structure of this ring of quotients...

Primitive ring, Semiprimitive ring Prime ring, Semiprime ring, Reduced ring Integral domain, Domain (ring theory) Field of fractions, Integral closure Euclidean...

Capable group Dedekind group Retract (group theory) Radical of a ring Semiprime ring Nielsen-Schreier theorem O'Connor, John J.; Robertson, Edmund F....

minimal ideals of a ring R, then N1N2 = {0}. A simple ring with a minimal right ideal is a semisimple ring. In a semiprime ring, there exists a minimal...

exists. By maximality of N, the quotient ring R/N has no nonzero nilpotent ideals, so R/N is a semiprime ring. As a result, N contains the lower nilradical...

Jacobson ring. The Baer radical of a ring is the intersection of the prime ideals of the ring R. Equivalently it is the smallest semiprime ideal in R...

number following 56 and preceding 58. It is a composite number. 57 is semiprime a Blum integer, and a Leyland number. The split Lie algebra E⁠7+1/2⁠ has...

(mod N). The structure of the RSA public key requires that N be a large semiprime (i.e., a product of two large prime numbers), that 2 < e < N, that e be...

a pronic number, a congruent number, a harmonic divisor number, and a semiprime. 6 is also the first Granville number, or S {\displaystyle {\mathcal {S}}}...

primary, and moreover an ideal is prime if and only if it is primary and semiprime (also called radical ideal in the commutative case). Every primary ideal...

numeric names: authors list (link) Martindale, Wallace S. (1973). "On semiprime P. I. Rings". Proceedings of the American Mathematical Society. 40 (2): 365...

sufficiently large even number can be expressed as the sum of a prime and a semiprime (the product of two primes). Also, any even integer greater than 10 can...

Fundamental theorem of arithmetic Factorization forms Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular...

must be greater than 1400. Almost prime Fermi–Dirac prime Perfect power Semiprime Crandall, Richard; Pomerance, Carl B. (2005). Prime Numbers: A Computational...

left) self-injective quasi-Frobenius prime, right (or left) primitive, semiprime, semiprimitive right (or left) (semi-)hereditary right (or left) nonsingular...

assume N = pq is a semiprime then the following process can be used to compute an eta-quotient basis of Mk(Γ0(N)). Fix a semiprime N = pq which is coprime...

and include principal ideal domains, Euclidean domains, and polynomial rings over a field. However, the theorem does not hold for algebraic integers...

{\displaystyle 110=5^{2}+6^{2}+7^{2}} . RSA-110 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. In base 10, the number 110...

{\displaystyle n} such that n + 2 {\displaystyle n+2} is either a prime or a semiprime and Iwaniec proved that there exist infinitely many integers n {\displaystyle...

If n {\displaystyle n} is a semiprime number (the product of two prime numbers) then the zero-divisor graph of the ring of integers modulo n {\displaystyle...

is a composite number and the first number which is neither prime nor semiprime. By Mihăilescu's Theorem, it is the only nonzero perfect power that is...

ISBN 978-0-521-82356-2, MR 2131318; see especially Lemma 8.2 (Ring Lemma), pp. 73–74, and Appendix B, The Ring Lemma, pp. 318–321. Knuth, Donald E (1997), The Art...

f(x)=x^{2}} over Z / b k Z {\displaystyle \mathbb {Z} /b^{k}\mathbb {Z} } , the ring of integers modulo b k {\displaystyle b^{k}} . As the inverse limit of Z...