2012/07/01 by N. S. Khripchenko
Mathematics · #Rings, Modules, and Algebras #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · doi:10.1080/00927872.2011.580441
Let 𝒞 be a pocategory, (see Khripchenko [3 Khripchenko , N. S. ( 2010 ). Finitary incidence algebras of quasiorders . Matematychni Studii 34 ( 1 ): 30 – 37 . [Google Scholar]]), and FI(𝒞) its finitary incidence ring [3 Khripchenko , N. S. ( 2010 ). Finitary incidence algebras of quasiorders . Matematychni Studii 34 ( 1 ): 30 – 37 . [Google Scholar]]. We prove that the ring ODer FI of outer derivations of FI(𝒞) is isomorphic to the ring ODer 𝒞 of outer derivations of 𝒞. Furthermore, if 𝒞 = 𝒞(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*(𝒞) [3 Khripchenko , N. S. ( 2010 ). Finitary incidence algebras of quasiorders . Matematychni Studii 34 ( 1 ): 30 – 37 . [Google Scholar]] are also described.