Thenecessary and sufficient conditions on the graph for which every maximal ideal is graded are discussed.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Let E be an arbitrary directed graph and let L be the Leavitt path algebra of the graph E over a field K.The necessary and sufficient conditions are given to assure the existence of a maximal ideal in L and also the necessaryand sufficient conditions on the graph that assure that every ideal is contained in a maximal ideal are given.
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Temel Bulgular & Veri:It is shownthat if a maximal ideal M of L is nongraded, then the largest graded ideal in M, namely gr(M) , is also maximalamong the graded ideals of L.
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Sonuç & Katkı:Thenecessary and sufficient conditions on the graph for which every maximal ideal is graded are discussed.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
Let E be an arbitrary directed graph and let L be the Leavitt path algebra of the graph E over a field K.The necessary and sufficient conditions are given to assure the existence of a maximal ideal in L and also the necessaryand sufficient conditions on the graph that assure that every ideal is contained in a maximal ideal are given. It is shownthat if a maximal ideal M of L is nongraded, then the largest graded ideal in M, namely gr(M) , is also maximalamong the graded ideals of L. Moreover, if L has a unique maximal ideal M, then M must be a graded ideal. Thenecessary and sufficient conditions on the graph for which every maximal ideal is graded are discussed.
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Bu Makaleye Atıf Yap
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