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Kernel Ideals in Semigroups

G. Sujatha*, Ch. Santhi Sundar Raj**, U. M. Swamy***

* Department of Mathematics, Jawaharlal Nehru Technological University Kakinada (JNTUK), Andhra Pradesh, India.

**-*** Department of Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India.

Periodicity:July - December'2024

Abstract

The concepts of *-ideals, strong ideals, *-congruences and kernel ideals are introduced in a pseudo-complemented semigroup and discussed certain properties of these. Some equivalent conditions for an ideal of a pseudocomplemented semigroup to become a kernel ideal are obtained. The lattice structure of strong ideals is discussed.

Keywords

Semigroup, Pseudo-Complemented Semigroup, *-Ideal, Strong Ideal, *-Congruence and Kernel Ideal.

How to Cite this Article?

Sujatha, G., Raj, Ch. S. S., and Swamy U. M. (2024). Kernel Ideals in Semigroups. i-manager’s Journal on Mathematics, 13(2), 22-31.

References

[1]. Birkhoff, G. (1940). Lattice Theory. American Mathematical Society.

[2]. Blyth, T. S. (1980). Ideals and filters of pseudo-complemented semilattices. Proceedings of the Edinburgh Mathematical Society, 23(3), 301-316.

[3]. Cornish, W. H. (1973). Congruences on distributive pseudocomplemented lattices. Bulletin of the Australian Mathematical Society, 8(2), 161-179.

[4]. Frink, O. (1962). Pseudo-complements in semi-lattices. Duke Mathematical Journal, 29(4), 505-514.

[5]. Glivenko, V. (1929). Sur quelques points de la logique de M. Brouwer. Bulletins de la Classe des Sciences, 15(5), 183-188.

[6]. Kist, J. (1963). Minimal prime ideals in commutative semigroups. Proceedings of the London Mathematical Society, 3(1), 31-50.

[7]. Stone, M. H. (1938). Topological representations of distributive lattices and Brouwerian logics. Journal of Mathematics and Physics Cultivation, 67 (1), 1–25.

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Kernel Ideals in Semigroups

Abstract

Keywords

How to Cite this Article?

References

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