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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Hazrat, Roozbeh and Vaš, Lia 2018. Baer and Baer *-ring characterizations of Leavitt path algebras. Journal of Pure and Applied Algebra, Vol. 222, Issue. 1, p. 39.
    VAŠ, LIA 2017. GRADED CHAIN CONDITIONS AND LEAVITT PATH ALGEBRAS OF NO-EXIT GRAPHS. Journal of the Australian Mathematical Society, p. 1.
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TRACES ON SEMIGROUP RINGS AND LEAVITT PATH ALGEBRAS

  • ZACHARY MESYAN (a1) and LIA VAŠ (a2)
Abstract

The trace on matrix rings, along with the augmentation map and Kaplansky trace on group rings, are some of the many examples of linear functions on algebras that vanish on all commutators. We generalize and unify these examples by studying traces on (contracted) semigroup rings over commutative rings. We show that every such ring admits a minimal trace (i.e., one that vanishes only on sums of commutators), classify all minimal traces on these rings, and give applications to various classes of semigroup rings and quotients thereof. We then study traces on Leavitt path algebras (which are quotients of contracted semigroup rings), where we describe all linear traces in terms of central maps on graph inverse semigroups and, under mild assumptions, those Leavitt path algebras that admit faithful traces.

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COPYRIGHT: © Glasgow Mathematical Journal Trust 2015 
References
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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