%0 Journal Article %T Primary Decompositions for Left Noetherian Rings %A V. V. Bavula %J Mathematics %D 2007 %I arXiv %X Two constructions are given that describe respectively all shortest primary decompositions and all shortest uniform decompositions for left Noetherian rings. They show that these decompositions are, in general, highly non-unique. %U http://arxiv.org/abs/math/0702028v1