Abstract local cohomology functors

We propose to define the notion of abstract local cohomology functors. The derived functors of the ordinary local cohomology functor with support in the closed subset defined by an ideal and the generalized local cohomology functor associated with a given pair of ideals are characterized as elements of the set of all the abstract local cohomology functors.Comment: To appear in Mathematical Journal of Okayama Universit

Local cohomology based on a nonclosed support defined by a pair of ideals

We introduce an idea for generalization of a local cohomology module, which we call a local cohomology module with respect to a pair of ideals (I,J), and study their various properties. Some vanishing and nonvanishing theorems are given for this generalized version of local cohomology. We also discuss its connection with the ordinary local cohomology.Comment: 28 pages, minor corrections, to appear in J. Pure Appl. Algebr

The torsion theory and the Melkersson condition

summary:We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring. In 2008 Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition in local cohomology theory. One of our purposes in this paper is to show how naturally the concept of Melkersson condition appears in the context of torsion theories

Magnetic-Field-Induced 4f-Octupole in CeB6 Probed by Resonant X-ray Diffraction

CeB6, a typical Gamma_8-quartet system, exhibits a mysterious antiferroquadrupolar ordered phase in magnetic fields, which is considered as originating from the T_{xyz}-type magnetic octupole moment induced by the field. By resonant x-ray diffraction in magnetic fields, we have verified that the T_{xyz}-type octupole is indeed induced in the 4f-orbital of Ce with a propagation vector (1/2, 1/2, 1/2), thereby supporting the theory. We observed an asymmetric field dependence of the intensity for an electric quadrupole (E2) resonance when the field was reversed, and extracted a field dependence of the octupole by utilizing the interference with an electric dipole (E1) resonance. The result is in good agreement with that of the NMR-line splitting, which reflects the transferred hyperfine field at the Boron nucleus from the anisotropic spin distribution of Ce with an O_{xy}-type quadrupole. The field-reversal method used in the present study opens up the possibility of being widely applied to other multipole ordering systems such as NpO2, Ce_{x}La_{1-x}B_{6}, SmRu_{4}P_{12}, and so on.Comment: 5 pages, 4 figures, submitte

A Case of Primary Signet-Ring Cell/Histiocytoid Carcinoma of the Eyelid: Immunohistochemical Comparison With the Normal Sweat Gland and Review of the Literature

Primary signet-ring cell/histiocytoid carcinomas of the eyelid are extremely rare tumors considered to originate from sweat glands. Here, we report the case of a 72-year-old man diagnosed with primary signet-ring cell/histiocytoid carcinoma of the eyelid and present immunohistochemical analyses of the eyelid apocrine gland (Moll gland) and apocrine and eccrine sweat glands of perineum and axilla. Widespread infiltration of tumor cells with signet-ring cell or histiocytoid appearance was observed in his left eyelid, orbit, and periocular lesion. Tumor cells expressed mucins and showed immunoreactivity that was similar to that of the Moll gland: MUC6 (+), GlcNAc alpha 1 -> 4Gal -> R(-), MUC2(-), MUC5AC(-), GCDFP15(+), CD15(+), S100(-), CK7(+), CK20(-), ER(+), PgR (+), HER2(-), E-cadherin(+), p63(-), PSA(-), and TTF-1(-). The tumor cells differed from those of perineal and axillary apocrine and eccrine sweat glands, which were MUC6(-). The Moll gland was ER(-) and PgR(-), whereas perineal and axillar apocrine sweat glands were ER(+) and PgR(+), and perineal and axillary eccrine sweat glands were ER(+) and PgR(-). The tumor showed characteristics similar to that of the eyelid Moll gland, which is demonstrated to be an apocrine gland with a protein expression distinct from that of other apocrine glands. MUC6 and GCDFP15 expression are useful in identifying the Moll gland immunophenotype and GCDFP15, ER and PgR expression are useful in distinguishing primary eyelid signet-ring/histocytoid carcinoma from gastrointestinal malignancies.ArticleAMERICAN JOURNAL OF DERMATOPATHOLOGY. 34(8):E139-E145 (2012)journal articl