The new concept"derimorphism"generalizing both derivation and homomor-phism is defined.When a derimorphism is invertible,its inverse is a Rota-Baxter operator.The general theory of derimorphism is establishe...The new concept"derimorphism"generalizing both derivation and homomor-phism is defined.When a derimorphism is invertible,its inverse is a Rota-Baxter operator.The general theory of derimorphism is established.The classification of all derimorphisms over an associative unital algebra is obtained.Contrary to the nonexistence of nontriv-ial positive derivations,it is shown that nontrivial positive derimorphisms do exist over any pair of opposite orderings over R[x],the lattice-ordered full matrix algebra and upper triangular matrix algebra over a totally ordered field.展开更多
基金Supported by NSFC under Grants 11771280 and 11671258by NSF of Shanghai Municipal under Grant 17ZR1415400.
文摘The new concept"derimorphism"generalizing both derivation and homomor-phism is defined.When a derimorphism is invertible,its inverse is a Rota-Baxter operator.The general theory of derimorphism is established.The classification of all derimorphisms over an associative unital algebra is obtained.Contrary to the nonexistence of nontriv-ial positive derivations,it is shown that nontrivial positive derimorphisms do exist over any pair of opposite orderings over R[x],the lattice-ordered full matrix algebra and upper triangular matrix algebra over a totally ordered field.
