Basic laws of the algebra of parallel compounds of N-poles

Any physical system interacting with the surrounding medium or with N-poles at N points ("poles") is called an N-pole (NP) N(X) in the present work. An autonomous physical system is called a zero-pole (0-pole). Mutually substitutable NP are said to be equivalent NP. Parallel combinations (P combinations) of P are denoted by the previous symbol [1]. On the basis of physical considerations, the basic laws of the algebra of P combinations of NP are taken to be the associative and commutative laws (Al) and (A2), i.e., axioms of each Abelian semigroup. As a consequence of laws (Al) and (A2), formulas analogous to certain axioms of linear algebra are obtained. The relation N(А)$\le$N(В) of shunt neutrality of N(A) with respect to N(B) is determined; a series of formulas expressing its basic properties is presented; it is asserted that they may be used in simplifying P combinations; and it is noted that this ratio is analogous to the inclusion relation $Х\subset Y$ of sets X and Y and also to the relation of partial order in semilattices (semistructures) and, in particular, in Boolean algebra.