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On S-principal right ideal rings
AIMS Mathematics, 2022 Let S be a multiplicative subset of a ring R. A right ideal A of R is referred to as S-principal if there exist an element s∈S and a principal right ideal aR of R such that As⊆aR⊆A.
Jongwook Baeck
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Short Principal Ideal Problem in multicubic fields
Journal of Mathematical Cryptology, 2020 One family of candidates to build a post-quantum cryptosystem upon relies on euclidean lattices. In order to make such cryptosystems more efficient, one can consider special lattices with an additional algebraic structure such as ideal lattices.
Lesavourey Andrea +2 more
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Overrings of Principal Ideal Domains [PDF]
Proceedings of the American Mathematical Society, 1971 All rings between a (right and left) principal ideal domain R R and its skewfield Q ( R ) Q(R) of quotients are quotient rings of R R with respect to Ore-systems in R R .
H. H. Brungs
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On Rings Whose Principal Ideals are Generalized Pure Ideals [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2007 This paper , introduces the notion of a right PIGP-ring (a ring in which every principal ideal of R is a GP-ideal ) with some of their basic properties ; we also give necessary and sufficient conditions for PIGP-rings to be a division ring and a regular ...
Husam Mohammad
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When is R[x] a principal ideal ring?
Revista Integración, 2018 Because of its interesting applications in coding theory, cryptography, and algebraic combinatoris, in recent decades a lot of attention has been paid to the algebraic structure of the ring of polynomials R[x], where R is a finite commutative ring with ...
Henry Chimal-Dzul, C. A. López-Andrade
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Proof That Certain Ideals in a Cyclotomic Realm are Principal Ideals [PDF]
Transactions of the American Mathematical Society, 1918 A theorem which serves to establish a connection between cyclotomy and the representation of numbers by quadratic forms is as follows: Let X represent a prime of the form 4n + 3, and q a prime that is congruent to 1, mod X. Further, let z a, z b represent the sums of those integers that are respectively quadratic residues and non-residues of X and that
Howard H. Mitchell
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Depth and regularity modulo a principal ideal [PDF]
Journal of Algebraic Combinatorics, 2018 20 pages, published version, Journal of Algebraic Combinatorics ...
Caviglia, Giulio +5 more
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On Rings Whose Principal Ideals are Pure [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2006 In this work, we study rings whose every principal ideal is a right pure. We give some properties of right PIP – rings and the connection between such rings and division rings.
Shaimaa Ahmad
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Principal Ideal Languages and Synchronizing Automata [PDF]
Fundamenta Informaticae, 2014 We study ideal languages generated by a single word. We provide an algorithm to construct a strongly connected synchronizing automaton for which such a language serves as the language of synchronizing words. Also we present a compact formula to calculate the syntactic complexity of this language.
Gusev, V. V. +2 more
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On the structure of principal ideal rings [PDF]
Pacific Journal of Mathematics, 1968 Thomas W. Hungerford
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