Cancellation properties of graded and nonunital rings. Graded clean and graded exchange Leavitt path algebras

DOI10.1142/S0219498823500500OpenAlexW3206958026MaRDI QIDQ5879290

Lia Vaš

Publication date: 28 February 2023

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.12031

zbMATH Keywords

clean ringgraded ringLeavitt path algebraexchange ringunit-regular ringcancellation propertiesgraded matrix algebranonunital ring

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Conditions on elements (16U99) Graded rings and modules (associative rings and algebras) (16W50) Leavitt path algebras (16S88)

Related Items (1)

On graded trinil clean rings

Cites Work

• Unnamed Item
• Unnamed Item
• Leavitt path algebras are graded von Neumann regular rings.
• The clean property is not a Morita invariant.
• Bass's first stable range condition
• Exchange Leavitt path algebras and stable rank
• Regularity conditions for arbitrary Leavitt path algebras.
• Lifting units in self-injective rings and an index theory for Rickart \(C^ *\)-algebras
• Extensions of exchange rings
• Methods of graded rings.
• Leavitt path algebras: graded direct-finiteness and graded \(\Sigma\)-injective simple modules
• Leavitt path algebras
• Graded cancellation properties of graded rings and graded unit-regular Leavitt path algebras
• Canonical traces and directly finite Leavitt path algebras.
• Refinements for infinite direct decompositions of algebraic systems
• Baer and Baer \(\ast\)-ring characterizations of Leavitt path algebras
• \(K\)-theory classification of graded ultramatricial algebras with involution
• Exchange rings and decompositions of modules
• Clean general rings.
• EXTENSIONS OF CLEAN RINGS
• A CHARACTERIZATION OF UNIT REGULAR RINGS
• Graded Rings and Graded Grothendieck Groups
• Corner Rings of a Clean Ring Need Not be Clean
• Extensions of Unit-Regular Rings
• Lifting Idempotents and Exchange Rings
• Exchange rings, units and idempotents
• On graded nil clean rings
• A CRASH COURSE ON STABLE RANGE, CANCELLATION, SUBSTITUTION AND EXCHANGE
• GRADED CHAIN CONDITIONS AND LEAVITT PATH ALGEBRAS OF NO-EXIT GRAPHS
• Imbedding a Regular Ring in a Regular Ring with Identity
• Group-regular rings

This page was built for publication: Cancellation properties of graded and nonunital rings. Graded clean and graded exchange Leavitt path algebras