Yazar "Rangaswamy, Kulumani M." seçeneğine göre listele

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    On intersections of two-sided ideals of Leavitt path algebras
    (Elsevier Science Bv, 2017) Esin, Songül; Er, Müge Kanuni; Rangaswamy, Kulumani M.
    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.
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    On Prüfer-like properties of Leavitt path algebras
    (World Scientific Publishing Co. Pte Ltd, 2019) Esin, Songül; Er, Müge Kanuni; Koç, Ayten; Radler, Katherine; Rangaswamy, Kulumani M.
    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.