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Journal articles on the topic 'Ring theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Xue, Zeqi. "Group Theory and Ring Theory." Journal of Physics: Conference Series 2386, no. 1 (2022): 012024. http://dx.doi.org/10.1088/1742-6596/2386/1/012024.

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Abstract Group theory is an important theory in abstract algebra. A ring is a kind of algebraic system with two operations (addition and multiplication). It has a deep relationship with groups, especially with the Abelian group. In this essay, the ring and the residual class ring will be talked about. Firstly, this passage is aim to talk about some basic knowledge about the ring which will let readers have a basic understanding of a ring. Then this passage will discuss the residual class ring and subring of the residual class ring of modulo. Some concepts about the ring are also mentioned, suc

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2

Baker, Ron. "Ring theory." New Scientist 217, no. 2898 (2013): 27. http://dx.doi.org/10.1016/s0262-4079(13)60045-7.

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3

Goldman, Michael A. "Ring theory." Nature 432, no. 7018 (2004): 674–75. http://dx.doi.org/10.1038/432674b.

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4

Matson, John. "Ring Theory." Scientific American 308, no. 2 (2013): 15. http://dx.doi.org/10.1038/scientificamerican0213-15a.

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5

Kozhukhov, I. B. "Technique of semigroup ring theory: Regular semigroup rings." Journal of Mathematical Sciences 95, no. 4 (1999): 2317–27. http://dx.doi.org/10.1007/bf02169100.

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6

Jung, Da Woon, Tai Keun Kwak, Min Jung Lee, and Yang Lee. "Ring properties related to symmetric rings." International Journal of Algebra and Computation 24, no. 07 (2014): 935–67. http://dx.doi.org/10.1142/s0218196714500428.

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The study of symmetric rings has important roles in ring theory and module theory. We investigate the structure of ring properties related to symmetric rings and introduce H-symmetric and π-symmetric as generalizations. We construct a non-symmetric reversible ring whose basic structure is infinite-dimensional, comparing with the finite-dimensional such rings of Anderson, Camillo and Marks. The structure of π-reversible rings (with or without identity) of minimal order is completely investigated. The properties of zero-dividing polynomials over IFP rings are studied more to show that polynomial

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7

Formanek, Edward. "Book Review: Ring theory." Bulletin of the American Mathematical Society 20, no. 2 (1989): 196–99. http://dx.doi.org/10.1090/s0273-0979-1989-15762-5.

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8

Michel, F. Curtis. "Planetary Ring: Another Theory." Physics Today 40, no. 10 (1987): 160–62. http://dx.doi.org/10.1063/1.2820253.

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9

Rota, Gian-Carlo. "Dimensions of ring theory." Advances in Mathematics 71, no. 1 (1988): 131. http://dx.doi.org/10.1016/0001-8708(88)90074-6.

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10

Elleaume, P. "Storage ring FEL theory." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 237, no. 1-2 (1985): 28–37. http://dx.doi.org/10.1016/0168-9002(85)90326-2.

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11

Richardson, Jeremy O. "Ring-polymer instanton theory." International Reviews in Physical Chemistry 37, no. 2 (2018): 171–216. http://dx.doi.org/10.1080/0144235x.2018.1472353.

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12

Kuiken, H. K., E. P. A. M. Bakkers, H. Ligthart, and J. J. Kelly. "The Rotating Ring-Ring Electrode. Theory and Experiment." Journal of The Electrochemical Society 147, no. 3 (2000): 1110. http://dx.doi.org/10.1149/1.1393321.

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13

Bakuradze, Malkhaz, and Mamuka Jibladze. "MoravaK-theory rings for the groupsG38, …,G41of order 32." Journal of K-Theory 13, no. 1 (2013): 171–98. http://dx.doi.org/10.1017/is013011009jkt245.

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AbstractB. Schuster [19] proved that themod2 MoravaK-theoryK(s)*(BG) is evenly generated for all groupsGof order 32. For the four groupsGof order 32 with the numbers 38, 39, 40 and 41 in the Hall-Senior list [11], the ringK(2)*(BG) has been shown to be generated as aK(2)*-module by transferred Euler classes. In this paper, we show this for arbitrarysand compute the ring structure ofK(s)*(BG). Namely, we show thatK(s)*(BG) is the quotient of a polynomial ring in 6 variables overK(s)*(pt) by an ideal for which we list explicit generators.

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14

Tunc¸ay, Mesut, and Aslihan Sezgin. "Soft Union Ring and its Applications to Ring Theory." International Journal of Computer Applications 151, no. 9 (2016): 7–13. http://dx.doi.org/10.5120/ijca2016911867.

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15

Carboni, Graciela, Jorge A. Guccione, and Juan J. Guccione. "Cohomology ring of differential operator rings." Journal of Algebra 339, no. 1 (2011): 55–79. http://dx.doi.org/10.1016/j.jalgebra.2011.05.017.

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16

Barnard, Tony, and P. M. Cohn. "An Introduction to Ring Theory." Mathematical Gazette 85, no. 503 (2001): 362. http://dx.doi.org/10.2307/3622065.

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17

Zelikin, M. I. "Fractal theory of Saturn’s ring." Proceedings of the Steklov Institute of Mathematics 291, no. 1 (2015): 87–101. http://dx.doi.org/10.1134/s008154381508009x.

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18

Farkas, Daniel R., and Gail Letzter. "Ring theory from symplectic geometry." Journal of Pure and Applied Algebra 125, no. 1-3 (1998): 155–90. http://dx.doi.org/10.1016/s0022-4049(96)00117-x.

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19

Okayama, Hideaki. "Ring Light Beam Deflector: Theory." Optical Review 10, no. 4 (2003): 283–86. http://dx.doi.org/10.1007/s10043-003-0283-5.

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20

Zhang, Jianluo, and John W. Y. Lit. "Compound fiber ring resonator: theory." Journal of the Optical Society of America A 11, no. 6 (1994): 1867. http://dx.doi.org/10.1364/josaa.11.001867.

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21

Richardson, Jeremy O. "Perspective: Ring-polymer instanton theory." Journal of Chemical Physics 148, no. 20 (2018): 200901. http://dx.doi.org/10.1063/1.5028352.

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22

Boeyens, J. C. A., and D. G. Evans. "Group theory of ring pucker." Acta Crystallographica Section B Structural Science 45, no. 6 (1989): 577–81. http://dx.doi.org/10.1107/s0108768189008189.

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23

Ding, Nanqing, Tai Keun Kwak, Fang Li, and Masahisa Sato. "Ring Theory and Related Topics." Frontiers of Mathematics in China 11, no. 4 (2016): 763–64. http://dx.doi.org/10.1007/s11464-016-0568-1.

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24

Banaschewski, B. "Ring theory and pointfree topology." Topology and its Applications 137, no. 1-3 (2004): 21–37. http://dx.doi.org/10.1016/s0166-8641(03)00196-2.

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25

Martinelli, Massimo, and Joseph C. Palais. "Theory of a tunable fiber ring depolarizer theory." Applied Optics 40, no. 18 (2001): 3014. http://dx.doi.org/10.1364/ao.40.003014.

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26

Kleiner, Israel. "From Numbers to Rings: The Early History of Ring Theory." Elemente der Mathematik 53, no. 1 (1998): 18–35. http://dx.doi.org/10.1007/s000170050029.

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27

Mustafa, Ibrahim, and Chnar Abdulkareem Ahmed. "ON NIL-SYMMETRIC RINGS AND MODULES SKEWED BY RING ENDOMORPHISM." Science Journal of University of Zakho 13, no. 3 (2025): 348–56. https://doi.org/10.25271/sjuoz.2025.13.3.1492.

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The symmetric property plays an important role in non-commutative ring theory and module theory. In this paper, we study the symmetric property with one element of the ring and two nilpotent elements of skewed by ring endomorphism on rings, introducing the concept of a right - -symmetric ring and extend the concept of right - -symmetric rings to modules by introducing another concept called the right - -symmetric module which is a generalization of -symmetric modules. According to this, we examine the characterization of a right - -symmetric ring and a right - -symmetric module and their relat

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28

Groechenig, Michael. "Adelic descent theory." Compositio Mathematica 153, no. 8 (2017): 1706–46. http://dx.doi.org/10.1112/s0010437x17007217.

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A result of André Weil allows one to describe rank $n$ vector bundles on a smooth complete algebraic curve up to isomorphism via a double quotient of the set $\text{GL}_{n}(\mathbb{A})$ of regular matrices over the ring of adèles (over algebraically closed fields, this result is also known to extend to $G$-torsors for a reductive algebraic group $G$). In the present paper we develop analogous adelic descriptions for vector and principal bundles on arbitrary Noetherian schemes, by proving an adelic descent theorem for perfect complexes. We show that for Beilinson’s co-simplicial ring of adèles

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29

Gálvez-Carrillo, Imma, and Sarah Whitehouse. "Central Cohomology Operations and K-Theory." Proceedings of the Edinburgh Mathematical Society 57, no. 3 (2014): 699–711. http://dx.doi.org/10.1017/s0013091513000680.

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AbstractFor stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP〈n⌰ for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory.

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30

Warren, Roger D. "The freeA-ring is a gradedA-ring." International Journal of Mathematics and Mathematical Sciences 16, no. 3 (1993): 617–19. http://dx.doi.org/10.1155/s0161171293000766.

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31

Berry, M. V., M. R. Jeffrey, and J. G. Lunney. "Conical diffraction: observations and theory." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2070 (2006): 1629–42. http://dx.doi.org/10.1098/rspa.2006.1680.

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Conical refraction was produced by a transparent biaxial crystal of KGd(WO 4 ) 2 illuminated by a laser beam. The ring patterns at different distances from the crystal were magnified and projected onto a screen, giving rings whose diameter was 265 mm. Comparison with theory revealed all predicted geometrical and diffraction features: close to the crystal, there are two bright rings of internal conical refraction, separated by the Poggendorff dark ring; secondary diffraction rings decorate the inner bright ring; as the distance from the crystal increases, the inner bright ring condenses onto an

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32

Basheer, Dr Muhammed. "Applications of Ring Theory in Post-Quantum Cryptography." International Journal for Research in Applied Science and Engineering Technology 13, no. 6 (2025): 294–301. https://doi.org/10.22214/ijraset.2025.71981.

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Post-quantum cryptography (PQC) aims to develop cryptographic protocols resistant to attacks by quantum computers, which threaten classical schemes based on integer factorization and discrete logarithm problems. Among various approaches, lattice-based cryptography has emerged as one of the most promising candidates for PQC. Within this domain, ring theory plays a foundational role by providing the algebraic structures—specifically polynomial rings modulo cyclotomic polynomials—used to define hard problems like Ring Learning With Errors (Ring-LWE). These problems underpin efficient and secure c

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33

Geiger, Joel, and Milen Yakimov. "Quantum Schubert cells via representation theory and ring theory." Michigan Mathematical Journal 63, no. 1 (2014): 125–57. http://dx.doi.org/10.1307/mmj/1395234362.

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34

Kozhukhov, I. B. "Techniques of semigroup ring theory: Artinian, perfect, and semiprimary semigroup rings." Journal of Mathematical Sciences 97, no. 6 (1999): 4527–37. http://dx.doi.org/10.1007/bf02364729.

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35

del Río, A. "Categorical methods in graded ring theory." Publicacions Matemàtiques 36 (July 1, 1992): 489–531. http://dx.doi.org/10.5565/publmat_362a92_15.

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36

Schofield, Aldan. "RING THEORY Volumes I and II." Bulletin of the London Mathematical Society 23, no. 1 (1991): 93–94. http://dx.doi.org/10.1112/blms/23.1.93.

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37

Goodearl, K. R. "Book Review: Dimensions of ring theory." Bulletin of the American Mathematical Society 20, no. 1 (1989): 107–13. http://dx.doi.org/10.1090/s0273-0979-1989-15718-2.

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38

Ye, Ming-Yong, and Xiu-Min Lin. "Theory of cavity ring-up spectroscopy." Optics Express 25, no. 26 (2017): 32395. http://dx.doi.org/10.1364/oe.25.032395.

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39

Foldes, Stephan. "Some ring theory from Jenő Szigeti." Miskolc Mathematical Notes 16, no. 1 (2015): 115. http://dx.doi.org/10.18514/mmn.2015.1726.

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40

Aihara, Jun-ichi. "Graph Theory of Ring-Current Diamagnetism." Bulletin of the Chemical Society of Japan 91, no. 2 (2018): 274–303. http://dx.doi.org/10.1246/bcsj.20170318.

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41

Yeh, Pochi. "Theory of unidirectional photorefractive ring oscillators." Journal of the Optical Society of America B 2, no. 12 (1985): 1924. http://dx.doi.org/10.1364/josab.2.001924.

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42

Van Oystaeyen, F. "Some applications of graded ring theory." Communications in Algebra 14, no. 8 (1986): 1565–96. http://dx.doi.org/10.1080/00927878608823385.

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43

Ypsilantis, T., and J. Seguinot. "Theory of ring imaging Cherenkov counters." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 343, no. 1 (1994): 30–51. http://dx.doi.org/10.1016/0168-9002(94)90532-0.

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44

Barnes, Edward O., Ana Fernández-la-Villa, Diego F. Pozo-Ayuso, et al. "Interdigitated ring electrodes: Theory and experiment." Journal of Electroanalytical Chemistry 709 (November 2013): 57–64. http://dx.doi.org/10.1016/j.jelechem.2013.10.009.

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45

Whelan, E. A. "An infinite construction in ring theory." Glasgow Mathematical Journal 30, no. 3 (1988): 349–57. http://dx.doi.org/10.1017/s001708950000745x.

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In this note we describe a class of functors on the category of associative rings with unity (hereafter “rings”) and of ring homomorphisms which, loosely speaking, ‘preserve the properties’ of two-sided ideals, but can be chosen to be arbitrarily ‘bad’ for one-sided properties of rings.

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46

Whelan, E. A. "An Infinite Construction in Ring Theory." Glasgow Mathematical Journal 33, no. 1 (1991): 121–23. http://dx.doi.org/10.1017/s0017089500008119.

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1. Point (3) of the main theorem of our paper [3, Theorem 1.1] is incorrect: this note corrects the main and consequential errors, and shows that (after minor adjustments) almost all the other results of [3], including the remaining seven points of Theorem 1.1, remain correct.2. The theme of [3] was a family of functors G,(–), defined on the category of rings with unity for each cardinal t. For t = 0, 1, the results of [3] are unchanged, but, for 2≤t<∞, major, and, for t infinite, less major, corrections are necessary; we therefore assume 2≤t. Terminology and notation are standard or as in

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47

Lizasoain, I., and G. Ochoa. "Clifford theory on the Burnside ring." Archiv der Mathematik 67, no. 3 (1996): 183–91. http://dx.doi.org/10.1007/bf01195233.

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48

DuPont, Marcus, Andrew MacFadyen, and Re’em Sari. "On the Theory of Ring Afterglows." Astrophysical Journal 957, no. 1 (2023): 29. http://dx.doi.org/10.3847/1538-4357/acffbc.

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Abstract Synchrotron and inverse Compton emission successfully explain the observed spectra of gamma-ray burst (GRB) afterglows. It is thought that most GRBs are products of extremely relativistic outflows and the afterglow marks the interaction of that ejecta with the surrounding matter. A faster decay of afterglow light curves at late times is indicative of nonspherical geometries, and is usually interpreted as evidence for jet geometry. Recent numerical simulations have shown that ring-like geometries are also permissible for relativistic outflows. We therefore extend the standard theory of

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49

Ramani, Vimala. "K-theory of oriented flag manifolds." Mathematica Slovaca 75, no. 2 (2025): 415–42. https://doi.org/10.1515/ms-2025-0031.

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Abstract We compute the complex K-ring of oriented flag manifolds F̃(n 1, … , nk ), k ≥ 3, of type (n 1, … , nk ). We use the representation theory of spinor groups and the Hodgkin spectral sequence for the computation of the K-ring.

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50

Garkusha, Grigory. "Correspondences and stable homotopy theory." Transactions of the London Mathematical Society 10, no. 1 (2023): 124–55. http://dx.doi.org/10.1112/tlm3.12056.

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AbstractA 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 is recovered from modules over a commutative symmetric ring spectrum defined in terms of framed correspondences over an algebraically closed field. Another application recovers stable motivic homotopy theory from spectral modules over associated spectral categories.

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