On uniform ideals and finite Goldie dimension in $R$-groups
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Keywords:
Nearring, essential ideal, uniform ideal, finite dimensionAbstract
We consider an $R$-group $G$, where $R$ is a (right) nearring. We introduce the notions relative uniform and strictly relative uniform ideals (or $R$-subgroup) which are not uniform, in general. We prove important properties and obtain a characterization for an $R$-subgroup to have finite Goldie dimension, in terms of strictly relative uniform $R$-subgroups. We provide the necessary examples.
References
Anderson F. W, Fuller, K. R, Rings and categories of modules, Graduate Texts in Mathematics, Springer-Verlag
New York, 13, 1992.
Badawi A, On weakly semiprime ideals of commutative rings. Beitr Algebra Geom 57, 589–597, 2016.
Bhavanari S., Contributions to near-ring theory, Doctrol Thesis, Nagarjuna University, India, 1984.
Bhavanari S., On modules with finite Goldie Dimension, J. Ramanujan Math. Soc. 5(1), 61-75, 1990.
Bhavanari S. and Guntupalli K.R., On a class of modules and N-groups. J. of Indian Math. Soc, 59, 39-44,
Bhavanari S., and Kuncham S.P., On direct and inverse systems in N-groups, Indian J. Math., 42(2), 183-192,
Bhavanari S. and Kuncham S.P., On Finite Goldie Dimension of Mn(N)-Group Nn, In: Proceedings of the
Conference on Nearrings and Nearfields, July 27–August 3, 2003, Hamburg, Germany.
Bhavanari S., and Kuncham S.P., Linearly independent elements in N-groups with Finite Goldie Dimension,
Bull. Korean Math. Soc., 42(3), 433-441, 2005.
Bhavanari S., Kuncham S.P., On finite Goldie dimension of Mn(N)-group Nn, Nearrings and
Nearfields,(Springer) 301-310, 2005.
Bhavanari S., and Kuncham S.P., Nearrings, fuzzy ideals, and graph theory. CRC press, 2013.
Bhavanari S., Kuncham S.P., Paruchuri V.R., and Mallikarjuna B., A note on dimensions in R-groups, Italian
Journal of Pure and Applied Mathematics, 44, 649-657, 2020.
Booth, G.L. and Groenewald, N.J., On primeness in matrix near-rings. Arch. Math., 56(6), 539-546, 1991.
Davoudian, M., 2019. On Pseudo-uniform modules, Palest. J. Math., 8(2), 15-21, 2019.
Goldie A.W., The structure of noetherian rings, Lectures on Rings and Modules, vol 246. Springer, Berlin,
Heidelberg, 1972.
Juglal, S., Groenewald, N. J., and Lee, K. S. E., Different prime R-ideals, Algebra Colloq., 17(1), 887-904, 2010.
Meldrum, J.D.P., Van der Walt, A.P.J.,Matrix near-rings, Arch. Math. 47(4), 312–319 (1986)
Meldrum, J.D.P., Near-rings and their links with groups, Bull. Amer. Math. Soc., 17, 156-160, 1985.
Nayak Hamsa, Kuncham S.P., Kedukodi B.S., ΘΓ-N-group, Matematicki Vesnik, 70(1), 64-78, 2018.
Nayak Hamsa, Kedukodi B.S, and Kuncham S.P., On central Boolean rings and Boolean type fuzzy ideals,
Kuwait J. Sci., 46(4), 23-32, 2019.
Oswald A., Near-rings in which every N-subgroup is principal, Proc. Lond. Math. Soc., 3(1), 67-88, 1974.
Pilz Gunter, Near-Rings: the theory and its applications, 23, North Holland, 1983.
Reddy Y.V., Bhavanari S., A note on N-Groups, Indian J. Pure Appl. Math., 19(9), 842-845, 1988.
Tapatee S, Kedukodi BS, Shum KP, Harikrishnan PK, Kuncham SP (2021) On essential elements in a lattice
and Goldie analogue theorem. Asian-Eur. J. Math. 2250091. https://doi.org/10.1142/S1793557122500917
Tapatee S., Kedukodi B.S., Shum K.P., Harikrishnan P.K., Kuncham S.P., On the finite Goldie dimension of
sum of two ideals of an R-group, Discussiones Mathematicae: General Algebra & Applications, 43(2), 177–187,
Tapatee S., Davvaz B., Harikrishnan P.K., Kedukodi B.S., Kuncham S.P., Relative Essential Ideals in R-groups,
Tamkang J. Math., 54, 69–82, 2023. https://doi.org/10.5556/j.tkjm.54.2023.4136
Tapatee S., Kedukodi B.S., Juglal S., Harikrishnan P.K., Kuncham S.P.: Generalization of prime ideals
in Mn(N)-group Nn, Rendiconti del Circolo Matematico di Palermo Series 2, 72(1), 449–465, 2023.
https://doi.org/10.1007/s12215-021-00682-y
Tapatee S., Meyer J.H., Harikrishnan P.K., Kedukodi B.S., Kuncham S.P., Partial Order in Matrix Nearrings.
Bull. Iranian Math. Soc., 48(6), 3195–3209, 2022. https://doi.org/10.1007/s41980-022-00689-w
Rajani, S., Tapatee, S., Harikrishnan, P.K., Kedukodi, B.S., Kuncham, S.P., Superfluous ideals
of N-groups, Rendiconti del Circolo Matematico di Palermo Series 2, 72(8), 4149–4167, 2023.
https://doi.org/10.1007/s12215-023-00888-2
Tapatee S., Harikrishnan P.K., Kedukodi B.S., Kuncham S.P., Graph with respect to superfluous elements in
a lattice, Miskolc Mathematical Notes, 23(2), 929-945, 2022. http://dx.doi.org/10.18514/MMN.2022.3620
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