Derivations of Finitary Incidence Rings
Author:
- 9 July 2012
- journal article
- research article
- Published byΒ Taylor & FrancisΒ inΒ Communications in Algebra
- Vol.Β 40 Β (7) , 2503-2522
Abstract
Let π be a pocategory, (see Khripchenko [ 3 Khripchenko , N. S. ( 2010 ). Finitary incidence algebras of quasiorders . Matematychni Studii 34 ( 1 ): 30 β 37 . [Google Scholar] ]), and FI(π) its finitary incidence ring [ 3 Khripchenko , N. S. ( 2010 ). Finitary incidence algebras of quasiorders . Matematychni Studii 34 ( 1 ): 30 β 37 . [Google Scholar] ]. We prove that the ring ODer FI of outer derivations of FI(π) is isomorphic to the ring ODer π of outer derivations of π. Furthermore, if π = π(P, R), where P is a quasiordered set and R is a ring, then it is proved that . As a consequence, the description of the algebra K-ODer FI of outer K-derivations of FI(P, A), where A is a K-algebra, is obtained. The ring of outer derivations and the algebra of outer K-derivations of the weak incidence ring I*(π) [ 3 Khripchenko , N. S. ( 2010 ). Finitary incidence algebras of quasiorders . Matematychni Studii 34 ( 1 ): 30 β 37 . [Google Scholar] ] are also described.Keywords
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