In this paper, we describe $ss$-supplement submodules in terms of a special class endomorphisms. Let $R$ be ring with semisimple radical and $P$ projective $R-$module. We show that there is bijection between ss-supplement $End_{R}(P)$. Moreover, define radical-s-projective modules as generalization modules. prove every submodule $R-$module over the radical. $SSI$-ring $R$, projective. provide r...

Abstract An explicit description of the ring rational polynomials in r indeterminates as a representation Lie algebra endomorphisms k -th exterior power countably infinite-dimensional vector space is given. Our based on results by Laksov and Throup concerning symmetric structure polynomial ring. are approximate versions vertex operators occurring celebrated bosonic representation, due to Date, ...

Assuming the Mumford–Tate conjecture, we show that center of endomorphism ring an abelian variety defined over a number field can be recovered from appropriate intersection fields obtained its Frobenius endomorphisms. We then apply this result to exhibit practical algorithm compute center.

We extend the characterization of virtual permutation endomorphisms in the case where IIi(Ai) = Zn. We show that for endomorphisms of Z[Zn] complexes the appropriate eigenvalue condition is that all eigenvalues be roots of units of the group ring Z[Zn\. Among these endomorphisms the virtual permutations are detected by Kq. The main application is in identifying Morse-Smale isotopy classes on th...

An abelian surface A is called a QM-abelian surface if its endomorphism ring includes an order of an indefinite quaternion algebra, and a curve C of genus two is called a QM-curve if its jacobian variety is a QMabelian surface. We give a computational result about the distribution of the arguments of the eigenvalues of the Frobenius endomorphisms of QM-abelian surfaces modulo good primes, which...

Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of Ep, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field Q(πp) generated by the Frobenius element πp. When the curve has complex multiplication (CM), this is always a fixed field as the prime varies. However, when the curve has no CM, very little is known, not...