Prime Factorization

Many questions about free ideal rings ( = firs, cf. [5] and §2 below) which at present seem difficult become much easier when one restricts attention to local rings. One is then dealing with hereditary local rings, and any such ring is in fact a fir (§2). Our object thus is to describe hereditary local rings. The results on firs in [5] show that such a ring must be a unique factorization domain; in §3 we prove that it must also be rigid (cf. the definition in [3] and §3 below). More precisely, for a semifir R with prime factorization rigidity is necessary and sufficient for R to be a local ring.

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Using Chaos in Grey Wolf Optimizer and Application to Prime Factorization

Advances in Intelligent Systems and Computing - Soft Computing for Problem Solving ◽

10.1007/978-981-13-1592-3_3 ◽

2018 ◽

pp. 25-43

Author(s):

Harshit Mehrotra ◽

Saibal K. Pal

Keyword(s):

Grey Wolf Optimizer ◽

Grey Wolf ◽

Prime Factorization

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Partial Orders, Lattices, Well-Founded Orderings, Unique Prime Factorization in ℤ and GCDs, Equivalence Relations, Fibonacci and Lucas Numbers, Public Key Cryptography and RSA, Distributive Lattices, Boolean Algebras, Heyting Algebras

Discrete Mathematics ◽

10.1007/978-1-4419-8047-2_5 ◽

2011 ◽

pp. 257-363

Author(s):

Jean Gallier

Keyword(s):

Public Key Cryptography ◽

Partial Orders ◽

Boolean Algebras ◽

Public Key ◽

Equivalence Relations ◽

Distributive Lattices ◽

Heyting Algebras ◽

Lucas Numbers ◽

Prime Factorization ◽

Fibonacci And Lucas Numbers

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An Optical System for Prime Factorization Based on Parallel Processing

Optical Supercomputing - Lecture Notes in Computer Science ◽

10.1007/978-3-642-22494-2_2 ◽

2011 ◽

pp. 10-15 ◽

Cited By ~ 1

Author(s):

Kouichi Nitta ◽

Osamu Matoba

Keyword(s):

Parallel Processing ◽

Optical System ◽

Prime Factorization

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