Скачать с ютуб If in a ring R, x^3=x for all x€R, then show that R is commutative. в хорошем качестве

If in a ring R, x^3=x for all x€R, then show that R is commutative.

#ring #abstractalgebra #mathatoz Mail:[email protected] Rajkishor Patra (M.Sc Jadavpur University)    / mathatozrkpatra   Please subscribe me🙏. If in a ring R, x^3=x for all x€R, then show that R is commutative.(Solution)    • Show that (x^2+1) is not a prime idea...   Proof of 'Principal ideal (x^2+1) is not a prime ideal of Z _2[x]'    • If R is a ring with no non zero nilpo...   If R is a ring with non zero nilpotent elements then show that for any idempotent element e,ex=xe for all x€R and thus e€Z(R).    • Let J={a+ib€Z[i]:a,b€7Z}. Show that J...   Let J={a+ib€Z[i]:a,b€7Z}. Show that J is an ideal of Z[i].Is J a maximal ideal? Also find the number of elements of Z[i]/J.(Bankura University -2022 based on maximal ideal).    • Is the mapping f:(z[√2],+,.) - (z[√3]...   This video contains an solution of a problem of ring theory of Bankura University -2019    • Prove that the rings Z and 2Z are not...   Two important exercises solution of ring theory of S K Mapa Higher Algebra .    • THIRD ISOMORPHISM THEOREM OF RING   This video contains Statement and proof of third Isomorphism theorem of ring with explanation.    • SECOND ISOMORPHISM THEOREM OF RING   This video contains Statement and proof of second isomorphism theorem of ring.    • FIRST ISOMORPHISM THEOREM OF RING.   This video contains statment and proof of First Isomorphism theorem of ring(Fundamental theorem of ring homomorphism)    • QUOTIENT RING OR FACTOR RING   This video contains definition of quotient ring or factor ring, important example.Statment and proof of such Theory which gives the relationship between quotient ring and prime Ideal and with maximal ideal.    • MAXIMAL IDEAL IN A RING   This video contains definition and important example of maximal ideal in a ring.The condition that a subring pZ is maximal ideal together with the proof.    • PRIME IDEAL OF RING   This video contains definition, example and property of prime ideal.The condition that an ideal of ring of integer be prime.    • PRINCIPAL IDEALS, PRINCIPAL IDEAL RIN...   This video contains definition and important example of principal ideal, principal ideal ring and principal ideal domain    • IDEAL OF RING (DEFINATION PROPERTY TH...   This video contains definition of Ideal different property, theory and important example.simple ring    • INTEGRAL DOMAIN(DEFINATION , PROPERTY...   This video contents definition of integral domain, it's important example property, related theory and their proof.    • Ring Theory (Abstract Algebra) CBCS S...   (This is the class:01 of ring Theory This video contents definition of ring and different property , theory example etc )    • RING THEORY (ABSTRACT ALGEBRA) CBCS S...   (This is Class:02 of Ring Theory .This video contents important definition, property, theory of ring Theory.This is very helpful for beginners )