Abstract
AbstractWe introduce the notion of a product fractal ideal of a ring using permutations of finite sets and multiplication operation in the ring. This notion generalizes the concept of an ideal of a ring. We obtain the corresponding quotient structure that partitions the ring under certain conditions. We prove fractal isomorphism theorems and illustrate the fractal structure involved with examples. These fractal isomorphism theorems extend the classical isomorphism theorems in rings, providing a broader viewpoint.
Funder
Manipal Academy of Higher Education, Manipal
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
Reference25 articles.
1. Aichinger, E., Binder, F., Ecker, J., Mayr, P., Nöbauer, C.: SONATA- System of Near-Rings and Their Applications, GAP Package, Version 2.8. http://www.algebra.uni-linz.ac.at/Sonata/ (2015)
2. Aishwarya, S., Kedukodi, B.S., Kuncham, S.P.: Commutativity in $$3$$-prime nearrings through permutation identities. Asian Eur. J. Math. 15(06), 2250109 (2022)
3. Anderson, F.W., Fuller, K.R.: Rings and categories of modules. In: Graduate Texts in Mathematics, vol. 13. Springer (1992)
4. Barnsley, M.F.: Fractals Everywhere, 2nd edn. Academic Press, New York (1993)
5. Bhavanari, S., Kuncham, S.P., Kedukodi, B.S.: Graph of a nearring with respect to an ideal. Commun. Algebra 38(5), 1957–1967 (2010)
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