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A Study on the Structure of Ideal-Based Non-Zero Divisor Graphs Associated with Zn [version 1; peer review: 2 approved] [PDF]
F1000ResearchBackground The study of algebraic structures through graph-theoretic representations provides a powerful visual and combinatorial framework for analyzing ring-theoretic properties. The ideal-based non-zero divisor graph ∅ I ( Z n ) , constructed from the
Ali Abd Aubad, Sameer Kadem
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Correspondences and stable homotopy theory [PDF]
Transactions of the London Mathematical Society, 2023 A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra SH is recovered from modules over a commutative symmetric ring ...
Grigory Garkusha
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Semidegenerate Congruence-modular Algebras Admitting a Reticulation
Scientific Annals of Computer Science, 2023 The reticulation L(R) of a commutative ring R was introduced by Joyal in 1975, then the theory was developed by Simmons in a remarkable paper published in 1980. L(R) is a bounded distributive algebra whose main property is that the Zariski prime
George Georgescu
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A generalization of CHSH and the algebraic structure of optimal strategies [PDF]
Quantum, 2020 $\textit{Self-testing}$ has been a rich area of study in quantum information theory. It allows an experimenter to interact classically with a black box quantum system and to test that a specific entangled state was present and a specific set of ...
David Cui +3 more
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Some results on PIT and GPIT theorems [PDF]
Journal of Hyperstructures, 2016 In this paper we generalize the P IT and the GP IT that can be used to study the heights of prime ideals in a general commutative Noetherian ring R and the dimension theory of such a ring and we use these generalizations to prove some useful results.
M. Ebrahimpour
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Generalizations of Multiplicative Ideal Theory to Commutative Rings with Zerodivisors
Bulletin of the Faculty of Science, Ibaraki University. Series A, Mathematics, 1985 Multiplicative ideal theories are studied for a commutative integral domain. We concern generalizations of these theories to a commutative ring with zero divisors. This paper is a synthetic report of the author's study on the area. The paper contains the solutions of open questions/conjectures of Griffin, Hinkle-Huckaba, Huckaba-Papick, Hutchins ...
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Exact solutions for the fractional differential equations by using the first integral method
Nonlinear Engineering, 2015 In this paper, we apply the first integral method to study the solutions of the nonlinear fractional modified Benjamin-Bona-Mahony equation, the nonlinear fractional modified Zakharov-Kuznetsov equation and the nonlinear fractional Whitham-Broer-
Aminikhah Hossein +2 more
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A class of hyperrings and hyperfields
International Journal of Mathematics and Mathematical Sciences, 1983 Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H.
Marc Krasner
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A GENERAL THEORY OF ZERO-DIVISOR GRAPHS OVER A COMMUTATIVE RING
International Electronic Journal of Algebra, 2016 Let R be a commutative ring with 1 6= 0, I a proper ideal of R, and ∼ a multiplicative congruence relation on R. Let R/∼ = { [x]∼ | x ∈ R } be the commutative monoid of ∼-congruence classes under the induced multiplication [x]∼[y]∼ = [xy]∼, and let Z(R/∼) be the set of zero-divisors of R/∼. The ∼-zero-divisor graph of R is the (simple) graph Γ∼(R) with
Anderson, David F., Lewis, Elizabeth F.
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Rayleigh-Schrödinger perturbation theory generalized to eigen-operators in non-commutative rings [PDF]
Journal of Mathematical Chemistry, 2010 A perturbation scheme to find approximate solutions of a generalized spectral problem is presented. The spectral problem is generalized in the sense that the ``eigenvalues'' searched for, are not real numbers but operators in a non-commutative ring, and the associated ``eigenfunctions'' do not belong to an Hilbert space but are elements of a module on ...
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