Properties of Generalised Lattice Ordered Groups

Penulis

  • Parimi Radha Krishna Kishore Arba Minch University
  • Dawit Cherinet Kifetew Arba Minch University

Kata Kunci:

Poset, lattice, po-group, l-group

Abstrak

A partially ordered group (po-group) is said to be a generalised lattice ordered group (gl-group) if the underlying poset is a generalised lattice. This paper is a study of some properties of finite subsets of a generalised lattice ordered group (gl-group). Finally obtained a lattice ordered group (l-group) from the given interally closed gl-group and concluded that every integrally closed gl-group is distributive.

Referensi

M. Murty and U. Swamy, “Distributive partially ordered sets,” The Aligarh Bull. of Math, vol. 8, pp. 1–16, 1978.

P. Kishore, M. Murty, V. Sri Ramani, and M. Patnaik, “On generalised lattices.” Southeast Asian Bulletin of Mathematics, vol. 33, no. 6, pp. 1091–1104, 2009.

P. Kishore, M. Murty, V. Sri Ramani, and M. Patnaik, “On generalised lattices.” Southeast Asian Bulletin of Mathematics, vol. 33, no. 6, pp. 23–26, 2009.

G. Birkhoff, Lattice theory. American Mathematical Soc., 1940, vol. 25.

V. Kopytov and N. Medvedev, The theory of lattice-ordered groups. Springer Science & Business Media, 2013, vol. 307.

S. Steinberg, Lattice-ordered rings and modules. Springer, 2010.

P. Kishore, “Generalised lattice ordered groups (gl-groups),” International Journal of Algebra, vol. 7, no. 2, pp. 63–68, 2013.

P. Kishore, “Ideals and congruences in a gl-group,” International Journal of Algebra, vol. 7, no. 2, pp. 69–72, 2013.

P. Kishore, “Generalised lattice ordered groupoids (gl–groupoids),” International journal of scientific and innovative mathematical research, vol. 2, no. 2, pp. 165–170, 2014.

Diterbitkan

2021-02-15

Cara Mengutip

Kishore, P. R. K., & Kifetew, D. C. (2021). Properties of Generalised Lattice Ordered Groups. (IJCSAM) International Journal of Computing Science and Applied Mathematics, 7(1), 25–27. Diambil dari https://journal.its.ac.id/index.php/ijcsam/article/view/4601

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