ZERO-DIVISORS AND IDEMPOTENTS IN QUANDLE RINGS

Bardakov, Valeriy G.; Passi, Inder Bir S.; Singh, Mahender

doi:https://doi.org/10.18910/88489

ZERO-DIVISORS AND IDEMPOTENTS IN QUANDLE RINGS

Bardakov, Valeriy G.; Passi, Inder Bir S.; Singh, Mahender

Osaka Journal of Mathematics, 2022, 59(3), 611-637

アクセス数:87件（2025-05-17 22:22 集計）

固定URL: https://doi.org/10.18910/88489

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論文情報

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タイトル	ZERO-DIVISORS AND IDEMPOTENTS IN QUANDLE RINGS
著者	著者名 Bardakov, Valeriy G.
	著者名 Passi, Inder Bir S.
	著者名 Singh, Mahender
抄録	The paper develops the theory of quandle rings introduced by the authors in a recent work. Orderability of quandles is investigated and many interesting examples of such quandles are given. It is proved that quandle rings of left or right orderable quandles which are semi-latin have nozero-divisors. Idempotents in quandle rings of certain interesting quandles are computed and used to determine sets of maximal quandles in these rings. Understanding of idempotents is further applied to determine automorphism groups of these quandle rings. Also, commutator width of quandle rings is introduced and computed in a few cases.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	59(3)
ページ	611-637
刊行年月	2022-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/88489
DOI	https://doi.org/10.18910/88489
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 59, Number 3 （2022-7）

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資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2022, 59(3), p. 611-637
DC.title	ZERO-DIVISORS AND IDEMPOTENTS IN QUANDLE RINGS
DC.creator	Bardakov, Valeriy G.
	Passi, Inder Bir S.
	Singh, Mahender
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2022-07
DCTERMS.abstract	The paper develops the theory of quandle rings introduced by the authors in a recent work. Orderability of quandles is investigated and many interesting examples of such quandles are given. It is proved that quandle rings of left or right orderable quandles which are semi-latin have nozero-divisors. Idempotents in quandle rings of certain interesting quandles are computed and used to determine sets of maximal quandles in these rings. Understanding of idempotents is further applied to determine automorphism groups of these quandle rings. Also, commutator width of quandle rings is introduced and computed in a few cases.
DC.identifier	10.18910/88489
DC.format	88489
citation_title	ZERO-DIVISORS AND IDEMPOTENTS IN QUANDLE RINGS
citation_author	Bardakov, Valeriy G.
	Passi, Inder Bir S.
	Singh, Mahender
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2022-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	59
citation_issue	3
citation_firstpage	611
citation_lastpage	637
citation_public_url	https://hdl.handle.net/11094/88489
citation_doi_detail	10.18910/88489
citation_doi	https://doi.org/10.18910/88489