… ideal that contains a ∗-homogeneous ideal is called potent and the same name bears a
domain all of whose maximal ∗-ideals … a ∗-ideal of finite type a ∗-homogeneous ideal, where …

… We conclude Section 2 with an estimate on the growth of vp(Ik), p ∈ Ass∞(I). We prove
that vp(Ik+1) ≤ vp(Ik) + ω(I), for all k ≫ 0. Thus, we have v(Ik+1) ≤ v(Ik) + ω(I) for k ≫ 0. …

… We show that by modifying the definition of a \(\star \)-homogeneous ideal we get a
theory of … -ideals of D. We define a nonzero finitely generated ideal I of D to be \(\star \)-homogeneous …

… *\)-ideal that contains a \(\star \)-homogeneous ideal is called … maximal \(\star \)-ideals are
potent. One among the various … \)-ideal of finite type a \(\star \)-homogeneous ideal, where and …

… the results on resurgence and asymptotic resurgence of homogeneous ideals in polynomial
rings. The computation of resurgence and asymptotic resurgence of cover ideals of finite …

… We show that J can be replaced by a monomial ideal. For this aim, let > be a monomial
order on V , and let in(J) be the initial ideal of J with respect to >. The natural K-basis of V/J …

… Our investigation is focused on the behavior of the function \({… t-th symbolic power of a
homogeneous ideal I in a noetherian … On the other hand, we show that if I is a monomial ideal such …

… We say that an ideal I on ω is homogeneous, if its restriction to any I-positive subset of ω is
… of homogeneous ideals and present some applications to topology and ideal convergence. …

… In Section 3, we concentrate our attention on the prime homogeneous ideal struc… homogeneous
ideals (Theorem 4.6). We also extend the study of chains of prime homogeneous ideals …

… on monomials according to the type of quasi-homogeneous polynomials we wish to deal with.
In the case where we are dealing with homogeneous ideals, … 2.3] - on which the following …