An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators

Let be the Weyl algebra and be the algebra of polynomial integro-differential operators over a field K of characteristic zero. The Conjecture/Problem of Dixmier (1968) [still open]: is an algebra endomorphism of the Weyl algebra A1 an automorphism? The aim of the paper is to prove that each algebra endomorphism of the algebra I1 is an automorphism. Notice that in contrast to the Weyl algebra A1 the algebra I1 is a non-simple, non-Noetherian algebra which is not a domain. Moreover, it contains infinite direct sums of nonzero left and right ideals.