Semiclassical limits of generic multiparameter quantized coordinate rings A = Oq(k) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric matrix whose entries generate a torsionfree subgroup of k×. A semiclassical limit of A is a Poisson algebra structure on the corresponding classical coordinate ring...

Semiclassical limits of generic multiparameter quantized coordinate rings A = Oq(k ) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric matrix whose entries generate a torsionfree subgroup of k. A semiclassical limit of A is a Poisson algebra structure on the corresponding classical coordinate ring...

‎‎we exhibit an explicit construction for the second cohomology group‎ ‎$h^2(l‎, ‎a)$ for a lie ring $l$ and a trivial $l$-module $a$‎. ‎we show how the elements of $h^2(l‎, ‎a)$ correspond one-to-one to the‎ ‎equivalence classes of central extensions of $l$ by $a$‎, ‎where $a$‎ ‎now is considered as an abelian lie ring‎. ‎for a finite lie‎ ‎ring $l$ we also show that $h^2(l‎, ‎c^*) cong m(l)$‎...

we introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. we firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. we next argue about the strong$alpha$-reversibility of some kinds of extensions. a number ofproperties of this version are established. it is shown ...

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...

in this paper, we introduce a class of rings which is a generalization of reversible rings. let r be a ring with identity. a ring r is called central reversible if for any a,b ∈ r, ab=0 implies ba belongs to the center of r. since every reversible ring is central reversible, we study sufficient conditions for central reversible rings to be reversible. we prove that some results of reversible ri...

We present a new method for computing the Igusa class polynomials of a primitive quartic CM field. For a primitive quartic CM field, K, we compute the Igusa class polynomials modulo p for certain small primes p and then use the Chinese remainder theorem and a bound on the denominators to construct the class polynomials. We also provide an algorithm for determining endomorphism rings of Jacobian...

Essential structural features of the high-pressure phase Ge32Co9−x: The atomic arrangement is built from a uniquely distorted cubic primitive Ge atoms. Ordered occupation neighboring cubes by Co atoms forms heteroatomic three-core clusters Co3Ge16. These units condense to form two interpenetrating frameworks interlinked covalent Ge−Ge bonds. homopolar germanium bonding creates characteristic si...

We extend to arbitrary commutative base rings a recent result of Demeneghi that every ideal an ample groupoid algebra over field is intersection kernels induced representations from isotropy groups, with much shorter proof, by using the author's Disintegration Theorem for representations. also prove primitive kernel representation group; however, we are unable show, in general, it irreducible r...