On Prüfer-like properties of Leavitt path algebras
| dc.contributor.author | Esin, Songül | |
| dc.contributor.author | Er, Müge Kanuni | |
| dc.contributor.author | Koç, Ayten | |
| dc.contributor.author | Radler, Katherine | |
| dc.contributor.author | Rangaswamy, Kulumani M. | |
| dc.date.accessioned | 2020-04-30T13:32:57Z | |
| dc.date.available | 2020-04-30T13:32:57Z | |
| dc.date.issued | 2019 | |
| dc.department | DÜ, Fen-Edebiyat Fakültesi, Matematik Bölümü | en_US |
| dc.description.abstract | Prüfer domains and subclasses of integral domains such as Dedekind domains admit characterizations by means of the properties of their ideal lattices. Interestingly, a Leavitt path algebra L, in spite of being noncommutative and possessing plenty of zero divisors, seems to have its ideal lattices possess the characterizing properties of these special domains. In [The multiplicative ideal theory of Leavitt path algebras, J. Algebra 487 (2017) 173-199], it was shown that the ideals of L satisfy the distributive law, a property of Prüfer domains and that L is a multiplication ring, a property of Dedekind domains. In this paper, we first show that L satisfies two more characterizing properties of Prüfer domains which are the ideal versions of two theorems in Elementary Number Theory, namely, for positive integers a,b,c, gcd(a,b) ·lcm(a,b) = a · b and a ·gcd(b,c) =gcd(ab,ac). We also show that L satisfies a characterizing property of almost Dedekind domains in terms of the ideals whose radicals are prime ideals. Finally, we give necessary and sufficient conditions under which L satisfies another important characterizing property of almost Dedekind domains, namely, the cancellative property of its nonzero ideals. © 2020 World Scientific Publishing Company. | en_US |
| dc.identifier.doi | 10.1142/S0219498820501224 | en_US |
| dc.identifier.issn | 0219-4988 | |
| dc.identifier.scopusquality | Q2 | en_US |
| dc.identifier.uri | https://dx.doi.org/10.1142/S0219498820501224 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12684/493 | |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | World Scientific Publishing Co. Pte Ltd | en_US |
| dc.relation.ispartof | Journal of Algebra and its Applications | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Leavitt path algebras; Prüfer domain | en_US |
| dc.title | On Prüfer-like properties of Leavitt path algebras | en_US |
| dc.type | Article | en_US |
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