Extension of MacMahon's Master Theorem to pre-semi-rings

An extended version of the classical MacMahon's "Master Theorem" to algebra ic structures 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-sen-ii-rings are not additive groups, such concepts as the de terminant of a matrix cannot be used any more, and the statement of the res ult itself has to be significantly different. When specialized to the field of real numbers, however, the extended result is shown to reduce to the cl assical version of MacMahon's "Master Theorem". (C) 2001 Elsevier Science I nc. All rights reserved.