ON WEAKLY NIL-SEMICOMMUTATIVE RINGS

‎We introduce the concept of weakly nil‎ - ‎semicommutative or WNSC rings and provide a condition that establishes the equivalence of WNSC rings to three generalised classes of semicommutative rings‎. ‎We prove the equivalence between WNSC Laurent polynomial rings and WNSC polynomial rings‎. ‎We supply examples of these classes of rings by considering Nagata and Dorroh extensions‎. ‎We also give a characterization for a ring of Morita context with zero pairings to be WNSC‎.