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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 icon 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 icon orcid.org/0000-0001-5325-4061 ; University of Maribor, Faculty of Economics and Business, Razlagova 14, SI-2000 Maribor, Slovenia
Burcu Ungor   ORCID icon orcid.org/0000-0001-7659-9185 ; Ankara University, Faculty of Sciences, Department of Mathematics, 06100 Tandogan, Ankara, Turkey

Puni tekst: engleski, pdf (158 KB) str. 177-190 preuzimanja: 147* citiraj
APA 6th Edition
Dolinar, G., Kuzma, B., Marovt, J. i Ungor, B. (2020). On some partial orders on a certain subset of the power set of rings. Glasnik matematički, 55 (2), 177-190. https://doi.org/10.3336/gm.55.2.01
MLA 8th Edition
Dolinar, Gregor, et al. "On some partial orders on a certain subset of the power set of rings." Glasnik matematički, vol. 55, br. 2, 2020, str. 177-190. https://doi.org/10.3336/gm.55.2.01. Citirano 06.12.2021.
Chicago 17th Edition
Dolinar, Gregor, Bojan Kuzma, Janko Marovt i Burcu Ungor. "On some partial orders on a certain subset of the power set of rings." Glasnik matematički 55, br. 2 (2020): 177-190. https://doi.org/10.3336/gm.55.2.01
Harvard
Dolinar, G., et al. (2020). 'On some partial orders on a certain subset of the power set of rings', Glasnik matematički, 55(2), str. 177-190. https://doi.org/10.3336/gm.55.2.01
Vancouver
Dolinar G, Kuzma B, Marovt J, Ungor B. On some partial orders on a certain subset of the power set of rings. Glasnik matematički [Internet]. 2020 [pristupljeno 06.12.2021.];55(2):177-190. https://doi.org/10.3336/gm.55.2.01
IEEE
G. Dolinar, B. Kuzma, J. Marovt i B. Ungor, "On some partial orders on a certain subset of the power set of rings", Glasnik matematički, vol.55, br. 2, str. 177-190, 2020. [Online]. https://doi.org/10.3336/gm.55.2.01

Sažetak
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.

Ključne riječi
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

Posjeta: 263 *