On intersections of two-sided ideals of Leavitt path algebras
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Dosyalar
Tarih
2017
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier Science Bv
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let E be an arbitrary directed graph and let L be the Leavitt path algebra of the graph E over a field K. It is shown that every ideal of L is an intersection of primitive/prime ideals in L if and only if the graph E satisfies Condition (K). Uniqueness theorems in representing an ideal of L as an irredundant intersection and also as an irredundant product of finitely many prime ideals are established. Leavitt path algebras containing only finitely many prime ideals and those in which every ideal is prime are described. Powers of a single ideal I are considered and it is shown that the intersection boolean AND(infinity)(n=1) I-n is the largest graded ideal of L contained in I. This leads to an analogue of Krull's theorem for Leavitt path algebras. (C) 2016 Elsevier B.V. All rights reserved.
Açıklama
Kanuni, Muge/0000-0001-7436-039X; Rangaswamy, Kulumani/0000-0001-9362-9913
WOS: 000387191700005
WOS: 000387191700005
Anahtar Kelimeler
Kaynak
Journal Of Pure And Applied Algebra
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
221
Sayı
3
