Extension of MacMahon's master theorem to pre-semi-rings
An extended version of MacMahon's master theorem in algebraic structures slightly more general than semi-rings namely pre-semi-rings (structures in which it is not necessary to assume the absorption property for the zero element) is postulated and proved. It is shown that the classical result may be generalized to commutative pre-semi-rings. But due to the fact that in such algebraic structures the existence of an additive or a multiplicative inverse for an element is no longer assumed the statement of the result must be changed and subsequently the concept of the determinant of a matrix cannot be used any more and it is necessary to make use of partial permutations. Finally, it is proved that the extended MacMahon's master theorem is reduced in the special case of the field of real numbers to the classical MacMahon's master theorem.
scientific article; zbMATH DE number 1705639
scientific article