Extension of MacMahonʹs Master Theorem to pre-semi-rings Original Research Article

An extended version of the classical MacMahonʹs “Master Theorem” to algebraicstructures much more general than the field of real numbers, namely semi-rings and even pre-semi-rings, is proposed. Due to the fact that many semi-rings or pre-semi-rings are not additive groups, such concepts as the determinant of a matrix cannot be used any more, and the statement of the result itself has to be significantly different. When specialized to the field of real numbers, however, the extended result is shown to reduce to the classical version of MacMahonʹs “Master Theorem”.