On the dimensions of graded rings (Q619023)

The author investigates some classical results on the Krull dimension (denoted by Kdim) of \(\mathbb{N}\)-graded commutative rings by using iterated boundary ideals and iterated boundary monoids. The same technique is used for characterizing the graded dimension (denoted by dimgr). The author establishes several results on boundary ideals which make him able to compare dimgr\(\mathcal{A}\), Kdim\(\mathcal{A}\) and Kdim(\(1+\mathcal{A}_{+})^{-1}\mathcal{A}\), where \(\mathcal{A}\) is a graded ring and \(\mathcal{A}_{+}\) is the augmentation ideal.