Prime decompositions of knots in

The famous H. Schubert theorem (1949) states that any nontrivial knot in S 3 admits a decomposition into connected sum of prime factors, which are unique up to order. We prove a similar result for knots in T × I , where T is a two-dimensional torus. However, we only consider knots of geometric degree one, use a different type of connected summation, and take into account the order of prime factors.