Interplay of Covered Quasi Ideals and Quasi Bases in Semigroup Theory


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Authors

  • Fahad Sikander Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Jeddah Branch-K.S.A
  • Shahnawaz Jamia Millia Islamia
  • M. Y. Abbasi Jamia Millia Islamia New Delhi
  • S. A. Khan Jamia Millia Islamia New Delhi

Keywords:

Covered quasi ideal, Greatest Covered quasi ideal, Maximal ideal, Quasi base; Semigroup

Abstract

This research article introduces and investigates the concepts of covered quasi ideals and quasi bases within the context of semigroup theory—a fundamental field of study in algebra. Covered quasi ideals represent a novel subset of semigroups, offering a versatile perspective that extends beyond conventional ideals, enabling a more flexible analysis of semigroup structures. In this paper, we delve into the properties and attributes of covered quasi ideals, providing a comprehensive exploration of their characteristics. Additionally, we establish intricate relationships between covered ideals, the greatest ideal, covered quasi ideals, and quasi bases, shedding light on the interconnections among these fundamental elements within the realm of semigroup theory.

References

I. Fabrici, Semigroups containing covered one-sided ideals, Mathematica Slovaca, 31(3) (1981), 225−231.

I. Fabrici, Semigroups containing covered two-sided ideals, Mathematica Slovaca, 34(4) (1984), 355−363.

I. Fabrici, One sided bases of semigroups, Matematicky Casopis, 22(4) (1972), 286−290.

I. Fabrici, On bases and maximal ideals in semigroups, Mathematica Slovaca, 31(2) (1981), 115−120.

S. Ozlu and A. S. Sezgin, Soft covered ideals in semigroups, Acta University Sapientiae Mathematica, 12(2) (2020),

−346.

M. F. Wu and X. Xiang. Yun, On C-ideals of ordered semigroups, Wuyi University jiangmen, 9 (1995), 43−46.

X. Xiang. Yun, On po-semigroups containing no maximal ideals, Southeast Asian Bulletin of Mathematics, 20(4) (1996),

−36.

T. Changphas and P. Summaprab, On ordered semigroups containing covered ideals, Communications in Algebra,

(9) (2016), 4104−4113.

M. F. Ali and N. M. Khan, Characterization of ordered semihypergroups by covered hyperideals, Kragujevac Journal

of Mathematics, 47(3) (2023), 417−429.

S. Omidi and B. Davvaz, C-Γ-hyperideal theory in ordered Γ-semihypergroups, Journal of Mathematical and

Fundamental Sciences, 49(2) (2017), 181−192.

S. A. Khan, M. Y. Abbasi and A. Ali, A study on covered lateral ideals of ordered ternary semigroups, Quasigroups and

Related Systems, 27(1) (2019), 73−76.

O. Steinfeld, Uber die quasiideale von halbgruppend, Publicationes Mathematicae Debrecen, 4 (1956), 262−275.

O. Steinfeld, Quasi-ideals in rings and semigroups, Budapest Hungary, (1978).

R. A. Good and D. R. Hughes, Associated groups for a semigroup, Bulletin of the American Mathematical Society, 58(6)

(1952), 624−625.

S. Lajos, On the bi-ideals in semigroups, Proceedings of the Japan Academy Ser A Mathematical Sciences, 45(8) (1969),

−712.

S . Lajos and F. A. Szasz, On the bi-ideals in assocoative ring, Proceedings of the Japan Academy Ser A Mathematical

Sciences, 49(6) (1970), 505−507.

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Published

2024-06-03

How to Cite

Fahad Sikander, Shahnawaz, M. Y. Abbasi, & S. A. Khan. (2024). Interplay of Covered Quasi Ideals and Quasi Bases in Semigroup Theory. Results in Nonlinear Analysis, 7(2), 43–52. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/386