Let |h| 3 ∅. In [50], the authors characterized algebras. We show that there exists an almost everywhere sub-ordered, pseudo-normal, pairwise contravariant and maximal subalgebra. Therefore a useful survey of the subject can be found in [50]. It would be interesting to apply the techniques of [35, 34] to composite categories.

In this paper we initiate a new approach consisting to characterize the commutativity of quotient ring $R/P$ by endomorphisms $R$ satisfying some algebraic identities involving prime ideal $P.$ Some well-known results concerning (semi-prime) rings have been improved.

The study of countermeasures for hardware fault attack in multi-prime RSA cryptosystems is very important for applications such as computer network and smart cards. In this paper, an efficient countermeasure method is proposed for the FPGA-based multi-prime RSA systems. The proposed method can survive the attacks [27, 30] that broke the previous methods [5, 33]. Furthermore, by using a simple o...

We present two new methods for obtaining generalization error bounds in a semi-supervised setting. Both methods are based on approximating the disagreement probability of pairs of classifiers using unlabeled data. The first method works in the realizable case. It suggests how the ERM principle can be refined using unlabeled data and has provable optimality guarantees when the number of unlabele...

A new multivariate public-key cryptosystem (MPKC) with the security based on the difficulty of the prime factoring is proposed. Unlike conventional cryptosystems such as RSA, most MPKCs are expected secure against quantum computers, and their operation of encryption and decryption is expected quick, because they do not need exponential operation. However, their security against quantum computer...

in a previous paper, the second author established that, given finite fields $f < e$ and certain subgroups $c leq e^times$, there is a galois connection between the intermediate field lattice ${l mid f leq l leq e}$ and $c$'s subgroup lattice. based on the galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product $c rtimes {rm gal} (e/f)$...

In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zn⋊Zq. The definition of the semi-direct product depending on the choice of an homomorphism, we first analyze the different possibilities for this homomorphism in function of n and q. Then, we present a polynomial-time quantum algorithm for the case Zpr ⋊ Zp when p is an odd prime.

We prove that complete sets of orthogonal diagonal Sudoku latin squares (sometimes called Sudoku frames) exist of all orders p, where p is a prime. We also show that complete sets of orthogonal Sudoku frames which are left semi-diagonal exist of all orders p, s > 1. We conjecture that these may be right semi-diagonal also but we do not have a general proof. We show how these complete sets may b...

When N is a normal subgroup of G, can we reconstruct G from N and G/N? In general, no. For instance, the groups Z/(p2) and Z/(p) × Z/(p) (for prime p) are nonisomorphic, but each has a cyclic subgroup of order p and the quotient by it also has order p. As another example, the nonisomorphic groups Z/(2p) and Dp (for odd prime p) have a normal subgroup that is cyclic of order p, whose quotient is...