<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Using a new definition, with respect to <xref ref-type="bibr" rid="j_auom-2018-0041_ref_021_w2aab3b7c11b1b6b1ab1ac21Aa">[21]</xref>, for normal hyperideals in Krasner (<italic>m, n</italic>)-hyperrings, we show that the corresponding quotient structures are (<italic>m, n</italic>)-rings. We prove equivalency of (strongly) regular and (strongly) compatible relations on <italic>n</italic>-ary hypergroups. Also, the connection between (<italic>m, n</italic>)-hyperfields and maximal normal hyperideals is investigated.</p></abstract>

Using a new definition, with respect to [21], for normal hyperideals in Krasner (m, n)-hyperrings, we show that the corresponding quotient structures are (m, n)-rings. We prove equivalency of (strongly) regular and (strongly) compatible relations on n-ary hypergroups. Also, the connection between (m, n)-hyperfields and maximal normal hyperideals is investigated.

Normal hyperideals in Krasner (<italic>m, n</italic>)-hyperrings

Department of Mathematics, Faculty of Basic Sciences

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Normal hyperideals in Krasner ()-hyperrings

{"article-title":{"italic":"m, n","content":["Normal hyperideals in Krasner (",")-hyperrings"]}}

Using a new definition, with respect to [21], for normal hyperideals in Krasner (m, n)-hyperrings, we show that the corresponding quotient structures are (m,...

Normal hyperideals in Krasner (m, n)-hyperrings

Published Online: Dec 31, 2018

Page range: 197 - 212

Received: Jun 18, 2017

Accepted: Jan 31, 2018

DOI: https://doi.org/10.2478/auom-2018-0041

Keywords
-hypergroup, Krasner ()-hyperring, Normal hyperideal

© 2018 Morteza Norouzi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Normal hyperideals in Krasner (m, n)-hyperrings

Published Online: Dec 31, 2018

Page range: 197 - 212

Received: Jun 18, 2017

Accepted: Jan 31, 2018

DOI: https://doi.org/10.2478/auom-2018-0041

Keywords-hypergroup, Krasner ()-hyperring, Normal hyperideal

© 2018 Morteza Norouzi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
-hypergroup, Krasner ()-hyperring, Normal hyperideal