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Two kinds of net operations, addition and Cartesian production of P/T nets, are introduced. Theyare defined on the set of underlying net of P/T systems. The conditions for preserving structural proper-ties of Petri net after these operations are discussed. It is shown that the set of P/T nets forms anAbelian group for net addition operation and the inverse net of a P/T net in usual meaning of net theo-ry is exactly the inverse of this P/T net as an element of the P/T net group; and that the set of P/Tnets forms an Abelian ring for net addition and Cartesian product operations.
Both kinds of net operations, addition and Cartesian production of P / T nets, are introduced. They are defined on the set of underlying net of P / T systems. The conditions for preserving structural proper- ties of Petri net after these operations are discussed. It is shown that the set of P / T nets forms an Abbelian group for net addition operation and the inverse net of a P / T net in the usual meaning of net theo-ry is exactly the inverse of this P / T net as an element of the P / T net group; and that the set of P / T ness forms an Abelian ring for net addition and Cartesian product operations.