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On perfect ideals of seminearrings

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Abstract

In this paper, we present the notion of perfect ideal of a seminearring S and prove that the kernel of a seminearring homomorphism is a perfect ideal. We show that the quotient structure S/I is isomorphic to the structure \(S_{T(I)}.\) Finally, we prove isomorphism theorems in seminearrings by using tame condition.

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References

  • Ahsan, J.: Seminear-rings characterized by their S-ideals, I. Proc. Jpn. Acad. Ser. A 71, 101–103 (1995a)

    MathSciNet  MATH  Google Scholar 

  • Ahsan, J.: Seminear-rings characterized by their S-ideals, II. Proc. Jpn. Acad. Ser. A 71, 111–113 (1995b)

    MathSciNet  MATH  Google Scholar 

  • Anderson, F.W., Fuller, K.R.: Rings and Categories of Modules. Springer, Berlin (1992)

    Book  Google Scholar 

  • Bennis, D., Fahid, B.: Rings in which every 2-absorbing ideal is prime. Beitr. Algebra Geom. 59, 391–396 (2018)

    Article  MathSciNet  Google Scholar 

  • Booth, G.L., Groenewald, N.J., Veldsman, S.: A Kurosh–Amitsur prime radical for near-rings. Commun. Algebra 18, 3111–3122 (1990)

    Article  MathSciNet  Google Scholar 

  • Church, A.: An unsolvable problem of elementary number theory. Am. J. Math. 58, 354–363 (1936)

    Article  MathSciNet  Google Scholar 

  • Gilbert, N.D., Samman, M.: Clifford semigroups and seminear-rings of endomorphisms. Int. Electron. J. Algebra 7, 110–119 (2010)

    MathSciNet  MATH  Google Scholar 

  • Gilbert, N.D., Samman, M.: Endomorphism seminear-rings of Brandt semigroups. Commun. Algebra 38, 4028–4041 (2010)

    Article  MathSciNet  Google Scholar 

  • Golan, J.S.: Semirings and their Applications. Kluwer Acadamic Publishers, Dordrecht (1999)

    Book  Google Scholar 

  • Hamed, A., Malek, A.: S-prime ideals of a commutative ring. Beitr. Algebra Geom. 61, 533–542 (2019). https://doi.org/10.1007/s13366-019-00476-5

    Article  MathSciNet  MATH  Google Scholar 

  • Henk, B., Erik, B.: Introduction to lambda calculus. Nieuw archief voor wisenkunde. 4, 337–372 (1984)

    MathSciNet  Google Scholar 

  • Jun, Y.B., Kim, K.: On structures of gamma-seminearrings. Int. Math. J. 1(1), 97–103 (2002)

    MathSciNet  Google Scholar 

  • Kedukodi, B.S., Kuncham, S.P., Bhavanari, S.: C-prime fuzzy ideals of Rn[x]. Int. J. Contemp. Math. Sci. 8, 133–137 (2013)

    Article  MathSciNet  Google Scholar 

  • Khan, W.A., Taouti, A., Karkain, S., Salami, A., Arif, W.: Weakly prime and weakly primary ideals in gamma seminearrings. Eur. J. Pure Appl. Math. 12, 544–552 (2019)

    Article  MathSciNet  Google Scholar 

  • Koppula, K., Kedukodi, B.S., Kuncham, S.P.: On prime strong ideals of a seminearring. Math. Vesnik. 72, 243–56 (2020)

    MathSciNet  MATH  Google Scholar 

  • Kornthorng, N., Iampan, A.: A note on right full k-ideals of seminearrings. J. Inform. Math. Sci. 3, 255–261 (2012)

    Google Scholar 

  • Krishna, K.V., Chatterjee, N.: A necessary condition to test the minimality of generalized linear sequential machines using the theory of near-semirings. Algebra Discrete Math. 3, 30–45 (2005)

    MathSciNet  MATH  Google Scholar 

  • Krishna, K.V., Chatterjee, N.: Representation of near-semirings and approximation of their categories. Southeast Asian Bull. Math. 31, 903–914 (2007)

    MathSciNet  MATH  Google Scholar 

  • Kuncham, S.P., Kedukodi, B.S., Harikrishnan, P., Bhavanari, S.: Nearrings, Nearfields and Related Topics. World Scientific, Singapore (2016)

    Google Scholar 

  • Mukherjee, R., Pal, P., Sardar, S.K.: On additively completely regular seminearrings. Commun. Algebra 45, 5111–5122 (2017)

    Article  MathSciNet  Google Scholar 

  • Mukherjee, R., Pal, P., Manna, T., Sardar, S.K.: On additively completely regular seminearrings-II. Commun. Algebra. 47, 5 (2019). https://doi.org/10.1080/00927872.2018.1524011

    Article  MathSciNet  MATH  Google Scholar 

  • Nayak, H., Kedukodi, B.S., Kuncham, S.P.: On central Boolean rings and Boolean type fuzzy ideals. Kuwait J. Sci. 46, 23–32 (2019)

    MathSciNet  MATH  Google Scholar 

  • Nayak, H., Kuncham, S.P., Kedukodi, B.S.: Extensions of Boolean rings and nearrings. J. Sib. Fed. Univ. Math. Phys. 12, 58–67 (2019)

    Article  MathSciNet  Google Scholar 

  • Omidi, S., Davvaz, B.: Fundamentals of derivations on (ordered) hyper(near)-rings. Beitr. Algebra Geom. 60, 537–553 (2019)

    Article  MathSciNet  Google Scholar 

  • Pilz, G.: Near-Rings: the Theory and its Applications. Revised Edition. North Hollond Publishing Company, Amsterdam (1983)

    MATH  Google Scholar 

  • Rojas, R.: A Tutorial Introduction to the Lambda Calculus. (1998). arXiv:1503.09060

  • Ravi, S.R., Cheruvu, K.: On quasi-regularity in gamma near-rings. Beitr. Algebra Geom. 60, 527–535 (2019)

    Article  MathSciNet  Google Scholar 

  • Sardar, S.K., Mukherjee, R.: On additively regular seminearrings. Semigroup Forum 88, 541–554 (2014)

    Article  MathSciNet  Google Scholar 

  • Van Hoorn, W.G., Van Rootselaar, B.: Fundamental notions in the theory of seminearrings. Compos. Math. 18, 65–78 (1967)

    MathSciNet  MATH  Google Scholar 

  • Veldsman, S.: On equiprime near-rings. Commun. Algebra. 20, 2569–2587 (1992)

    Article  MathSciNet  Google Scholar 

  • Weinert, H.J.: Seminearrings, seminearfields and their semigroup-theoretical background. Semigroup Forum 24, 231–254 (1982)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors acknowledge reviewers for their valuable comments and suggestions. Authors also acknowledge the support and encouragement of Manipal Institute of Technology, Manipal Academy of Higher Education, India.

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Authors and Affiliations

  1. Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, 576104, India

    Kavitha Koppula, Babushri Srinivas Kedukodi & Syam Prasad Kuncham

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  1. Kavitha Koppula
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  2. Babushri Srinivas Kedukodi
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  3. Syam Prasad Kuncham
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Correspondence to Babushri Srinivas Kedukodi.

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Koppula, K., Kedukodi, B.S. & Kuncham, S.P. On perfect ideals of seminearrings. Beitr Algebra Geom 62, 823–842 (2021). https://doi.org/10.1007/s13366-020-00535-2

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