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Ideals of Leavitt Path Algebras and ...

Radler, Katherine Marie.

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Ideals of Leavitt Path Algebras and Their Supersymmetric Analogues.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Ideals of Leavitt Path Algebras and Their Supersymmetric Analogues./
作者:	Radler, Katherine Marie.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:	68 p.
附註:	Source: Dissertations Abstracts International, Volume: 82-03, Section: B.
Contained By:	Dissertations Abstracts International82-03B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27999542
ISBN:	9798664761948

Ideals of Leavitt Path Algebras and Their Supersymmetric Analogues.
Radler, Katherine Marie.

Ideals of Leavitt Path Algebras and Their Supersymmetric Analogues. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 68 p.

Source: Dissertations Abstracts International, Volume: 82-03, Section: B.

Thesis (Ph.D.)--Saint Louis University, 2020.

This item must not be sold to any third party vendors.

Leavitt path algebras were developed in the early 2000s to answer Leavitt's question about algebras which do not have the Invariant Basis Number property. Since then a lot of work has been done in the development of the theory of Leavitt path algebras including ideal theory. In this dissertation we will discuss two current strands of research in Leavitt path algebra that we have worked on. We will go in depth into the ideal theory of Leavitt path algebras and how these properties coincide with properties of Prufer rings. In chapter two we will prove that the ideals in Leavitt path algebras satisfy an ideal analogue of the number theory property that the product of the least common multiple and greatest common factor of two numbers is equal to the product of those two numbers. In recent years there has been an interest in developing superalgebras of well known algebras. In this dissertation we will also discuss a supersymmetric analogue of Leavitt path algebras. In chaper 3, we will define Leavitt path superalgebras and prove supersymmetric analogues to well known theorems for Leavitt path algebras. In chapter 4, we will discuss the growth of Leavitt path algebras and the growth of Leavitt path superalgebras. We will find a basis for Leavitt path superalgebras as well as show that they have polynomial growth.

ISBN: 9798664761948Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Leavitt path algebras

Ideals of Leavitt Path Algebras and Their Supersymmetric Analogues.
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520 $a Leavitt path algebras were developed in the early 2000s to answer Leavitt's question about algebras which do not have the Invariant Basis Number property. Since then a lot of work has been done in the development of the theory of Leavitt path algebras including ideal theory. In this dissertation we will discuss two current strands of research in Leavitt path algebra that we have worked on. We will go in depth into the ideal theory of Leavitt path algebras and how these properties coincide with properties of Prufer rings. In chapter two we will prove that the ideals in Leavitt path algebras satisfy an ideal analogue of the number theory property that the product of the least common multiple and greatest common factor of two numbers is equal to the product of those two numbers. In recent years there has been an interest in developing superalgebras of well known algebras. In this dissertation we will also discuss a supersymmetric analogue of Leavitt path algebras. In chaper 3, we will define Leavitt path superalgebras and prove supersymmetric analogues to well known theorems for Leavitt path algebras. In chapter 4, we will discuss the growth of Leavitt path algebras and the growth of Leavitt path superalgebras. We will find a basis for Leavitt path superalgebras as well as show that they have polynomial growth.
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