A associative ring R with an unit element is called an Ivolutive RIng,if every element of the muttiplicative group U/(R),which consists of all the units of R,satisfies equation x^2=e,where e is the unit element of R.I...A associative ring R with an unit element is called an Ivolutive RIng,if every element of the muttiplicative group U/(R),which consists of all the units of R,satisfies equation x^2=e,where e is the unit element of R.In the paper,we have proved that the residue class ring Zn modulo n>1 is an involutive ring if and only if n are the following numbers:2,3,4,6,8,12,24.Moreover,we call a ring R is an U-cyclic ring if the unit group U(R)is a cyclic group.We have proved also that the involutive ring Zn modulo n>1 is an U-cyclic if and only if n are the following integer numers 2,3,4,6.展开更多
文摘A associative ring R with an unit element is called an Ivolutive RIng,if every element of the muttiplicative group U/(R),which consists of all the units of R,satisfies equation x^2=e,where e is the unit element of R.In the paper,we have proved that the residue class ring Zn modulo n>1 is an involutive ring if and only if n are the following numbers:2,3,4,6,8,12,24.Moreover,we call a ring R is an U-cyclic ring if the unit group U(R)is a cyclic group.We have proved also that the involutive ring Zn modulo n>1 is an U-cyclic if and only if n are the following integer numers 2,3,4,6.
