Rank conditions and amenability for rings associated to graphs

• We study path rings, Cohn path rings, and Leavitt path rings associated to directed graphs, with coefficients in an arbitrary ring R. For each of these types of rings, we stipulate conditions on the graph that are necessary and sufficient to ensure that the ring satisfies either the rank condition or the strong rank condition whenever R enjoys the same property. In addition, we apply our result for path rings and the strong rank condition to characterize the graphs that give rise to amenable path algebras and exhaustively amenable path algebras.

Subject headings

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Keyword

path ring

path algebra

Cohn path ring

Cohn path algebra

Leavitt path ring

Leavitt path algebra

rank condition

unbounded generating number

strong rank condition

amenable algebra

exhaustively amenable algebra

algebraically amenable algebra

properly algebraically amenable algebra

Mathematics and applications

Matematik med tillämpningar

Publication and Content Type

vet (subject category)

ovr (subject category)