We study the behavior of various properties of commutative Noetherian rings under Segre
products, with a special focus on properties in positive prime characteristic defined using the …

Full article: On the Frobenius Power and Colon Ideals Skip to Main Content Taylor and Francis
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In order to study graded Frobenius algebras from a ring theoretical perspective, we
introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the …

For a commutative ring R, the F-signature was defined by Huneke and Leuschke [Math. Ann.
324 (2)(2002) 391–404]. It is an invariant that measures the order of the rank of the free …

In this paper, we address a question concerning nilpotent Frobenius actions on Rees
algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke …

An excellent ring of prime characteristic for which the Frobenius map is pure is also
Frobenius split in many commonly occurring situations in positive characteristic commutative …

The notion of tight closure of an ideal introduced by Hochster and Huneke [5] enables us to
define classes of singularities corresponding to rational singularities in characteristic 0 for …

In this paper we study the rings defined by ideals of pfaffians of a skew symmetric matrix of
indeterminates. We analyze the case in which the pfaffians are not necessarily of fixed size …

Let (R, 𝔪) be a 1-dimensional Cohen–Macaulay local ring of multiplicity e and embedding
dimension ν≥ 2. Let B denote the blowing-up of R along 𝔪 and let I be the conductor of R in …

Among reduced Noetherian prime characteristic commutative rings, we prove that a regular
ring is precisely that where the finite intersection of ideals commutes with taking bracket …