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Suppose that R is a commutative ring which has an identity. It has been shown that if B is an R-algebra such that a finite group G acts as R-linear automorphisms on B. [Here, is the subring of  consisting of row and column finite matrices  indexed by elements of G with entries in  defining a map  by  then,  is invariant. In this paper, we show further that   is convex. 

convexity, homomorphisms, commutative ring, isomorphism, finite matrices, linear automorphisms, subring.