For a class C of finite lattices, the question arises whether any lattice in C can be embedded into some atomistic, biatomic lattice in C. We provide answers to the question above for C being, respectively, — The class of all finite lattices; — The class of all finite lower bounded lattices (solved by the first author's earlier work). — The class of all finite join-semidistributive lattices (th...

The concepts of a prime ideal of a distributively generated (d.g.) nearring R, a prime d.g. near-ring and an irreducible R-group are introduced1). The annihilating ideal of an irreducible R-group with an R-generator is a prime ideal. Consequently we define a prime ideal to be primitively prime if it is the annihilating ideal of such an R-group, and a d.g. near-ring to be a primitively prime nea...

The notions of quasi-embedding, quasi-equality, and quasi-isomorphism are generalized their properties studied.

We prove that if G is a non-uniform lattice in a rank-one semisimple Lie group = Isom(H2 R ), then G is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding G → G is coarsely surjective and thus is a quasi-isometry.

In this paper the authors provide a complete answer to Donkin’s Tilting Module Conjecture for all rank 2 2 semisimple algebraic groups and al...

An infinite f.g. group G is quasi-finitely axiomatizable (QFA) if there is a first-order sentence j such that G ! j, and if H is a f.g. group such that H ! j, then GGH. The first result is that all Baumslag–Solitar groups of the form ha; d j d"1ad 1⁄4 ai are QFA. A f.g. group G is a prime model if and only if there is a tuple g1; . . . ; gn generating G whose orbit (under the automorphisms of G...

Let K/F be a cyclic field extension of odd prime degree. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F ) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F )]-modules. For these embedding problems we prove conditions on solvability, formulas for explicit construction, and results on automatic realizability.

Miyaji, Nakabayashi and Takano (MNT) gave families of group orders of ordinary elliptic curves with embedding degree suitable for pairing applications. In this paper we generalise their results by giving families corresponding to non-prime group orders. We also consider the case of ordinary abelian varieties of dimension 2. We give families of group orders with embedding degrees 5, 10 and 12.

Problems of plaintext embedding on elliptic curve are considered in this paper. We present the embedding algorithm on binary field and make a comparison with it on prime field on performance. In the end we provide some applications on storage and transmission of points in elliptic curve.

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.