a survey on the fusible property of skew pbw extensions

We present several results that establish the fusible and the regular left fusible properties of the family of noncommutative rings known as skew poincaré-birkhoff-witt extensions. our treatment is based on the recent works of ghashghaei and mcgovern [13], and koşan and matczuk [31] concerning the left fusibleness and the regular left fusibleness of skew polynomial rings of automorphism type. since the results formulated in this paper can be applied to algebraic structures more general than skew polynomial rings, our contribution to the theory of fusibleness is to cover more families of rings of interest in branches as quantum groups, noncommutative algebraic geometry and noncommutative differential geometry. we provide illustrative examples of the ideas developed here.