We study the relation of the ideal class group of a Dedekind domain A to that of As, where S is a multiplicatively closed subset of A. We construct examples of (a) a Dedekind domain with no principal prime ideal and (b) a Dedekind domain which is not the integral closure of a principal ideal domain. We also obtain some qualitative information on the number of non-principal prime ideals in an ar...

Let $\mathfrak{g}$ be a semisimple Lie algebra. We establish new relation between the Goldie rank of primitive ideal $\mathcal{J}\subset U(\mathfrak{g})$ and dimension corresponding irreducible representation $V$ an appropriate finite W-algebra. Namely, we show that $\operatorname{Grk}(\mathcal{J}) \leqslant \dim V/d_V$, where $d_V$ is index suitable equivariant Azumaya algebra on homogeneous s...

We attach a Dixmier algebra B to the closure O of any nilpotent orbit of G where G is GL(n, C), O(n, C) or Sp(2n, C). This algebra B is a noncommutative analog of the coordinate ring R of O, in the sense that B has a G-invariant algebra filtration and grB = R. We obtain B by making a noncommutative analog of the Kraft-Procesi construction which modeled O as the algebraic symplectic reduction of...

which is impossible since r is a primitive root of I and the exponent is odd. 1 Proc. Nat. Acad. Sci., 15, 45 (1929). 2 We say that an ideal p belongs to an exponent n when p" is a principle ideal but pd is not a principal ideal for 0 < d < n. Trans. Amer. Math. Soc., 31, 632 (1929). Duke Math. Jour., 5, 419-420 (1939). 6 Trans. Amer. Math. Soc., 31, 632-633 (1929). 6 Dickson, Jour. fair. Math....

Gu map-1 is a modified version of GGH map. It uses same ideal lattices for constructing the trapdoors, while the novelty is that no encodings of zero are given. In this short paper we show that Gu map-1 cannot be used for the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. That is, if Gu map-1 is used for such instance, we can break it by soving a combined 3-...

It is well known that the set of all ideals(2) of a ring forms a complete modular lattice with respect to set inclusion. The same is true of the set of all right ideals. Our purpose in this paper is to consider the consequences of imposing certain additional restrictions on these ideal lattices. In particular, we discuss the case in which one or both of these lattices is complemented, and the c...

primitive  neuroectodermal  tumor  (pnet)  of  kidney  is  an  extremely  rare  renal  neoplasm  with only about fifty reported cases in literature.  presumably,of neural crest origin, these tumors behave  aggressively  and  carry  a  poor prognosis.  we  report  a  case  of  22-year  old  female  patient complaining of left loin pain with recurrent hematuria for last 3 months. on clinical exam...

An old question of T. Jech and K. Prikry asks if an existence of a precipitous ideal implies necessary existence of a normal precipitous ideal. The aim of the paper is to prove some results in the positive direction. Thus, it is shown that under some mild assumptions, an existence of a precipitous ideal over א1 implies an existence of a normal precipitous ideal over א1 once a Cohen subset is ad...