Original scientific paper

https://doi.org/10.3336/gm.55.2.01

On some partial orders on a certain subset of the power set of rings

Gregor Dolinar orcid.org/0000-0001-9083-5578 ; University of Ljubljana, Faculty of Electrical Engineering, Tržaška cesta 25, SI-1000 Ljubljana, Slovenia
Bojan Kuzma ; University of Primorska, Glagoljaška 8, SI-6000 Koper, Slovenia
Janko Marovt orcid.org/0000-0001-5325-4061 ; University of Maribor, Faculty of Economics and Business, Razlagova 14, SI-2000 Maribor, Slovenia
Burcu Ungor orcid.org/0000-0001-7659-9185 ; Ankara University, Faculty of Sciences, Department of Mathematics, 06100 Tandogan, Ankara, Turkey

Abstract

Let \(\mathcal{R}\) be a ring with identity and let $\mathcal{J}_{\mathcal{R}}$ be a collection of subsets of $\mathcal{R}$ such that their left and right annihilators are generated by the same idempotent. We extend the notion of the sharp, the left-sharp, and the right-sharp partial orders to $\mathcal{J}_{\mathcal{R}}$, present equivalent definitions of these orders, and study their properties. We also extend the concept of the core and the dual core orders to $\mathcal{J}_{\mathcal{R}}$, show that they are indeed partial orders when $\mathcal{R}$ is a Baer $\ast$-ring, and connect them with one-sided sharp and star partial orders.

Keywords

Baer $\ast$-ring; sharp partial order; core partial order; star partial order; one-sided partial order

Hrčak ID:

248655

URI

https://hrcak.srce.hr/248655

Publication date:

23.12.2020.

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