All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R(M), the idealization of M . Homogenous ideals of R(M) have the form I (+)N , where I is an ideal of R and N a submodule of M such that IM ⊆ N . A ring R (M) is called a homogeneous ring if every ideal of R (M) is homogeneous. In this paper we continue our recent work on the idealization of m...

There are two equivalent de nitions of a fuzzy right ideal, fuzzy left ideal, fuzzy bi-ideal or fuzzy quasi-ideal f of an ordered semigroup (or a semigroup) S in the bibliography. The rst one is based on the fuzzy subset f itself, the other on the multiplication of fuzzy sets and the greatest fuzzy subset of S. Investigations in the existing bibliography are based on the rst de nition. The pres...

We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.

By considering the notion of multiplication modules over a commutative ring with identity, first we introduce the notion product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module. Finally, we state and prove a version of Nakayama lemma for multiplication modules and find some related basic results. 1. Introduction. Let R b...

We characterize the compact multiplication operators on a semicrossed product $C_0(X)\times _\phi \mathbb Z_+$ in terms of corresponding dynamical system. also elements this algebra and determine ideal they generate.

Inspired by the discussion in [5], we study the multiplicative complexity and the rank of the multiplication in the local algebras Rm;n = k[x; y]=(xm+1; yn+1) and Tn = k[x; y]=(xn+1; xny; : : : ; yn+1) of bivariate polynomials. We obtain the lower bounds (2 13 o(1)) dimRm;n and (2 12 o(1)) dim Tn for the multiplicative complexity of the multiplication in Rm;n and Tn, respectively. On the other ...

Differences in the characteristics of the culture conditions can influence the multiplication rate of Plasmodium falciparum. The Petri dish method is one of the most popular methods of cultivating this parasite. In many previous studies, ideal culture conditions of the Petri dish method were achieved by using erythrocytes collected from blood that had been stored for at least 2 weeks, with dail...

We consider multi-party computation (MPC) in a hierarchical setting, where participants have different capabilities depending on their position in the hierarchy. First, we give necessary conditions for multiplication of secrets in a hierarchical threshold linear secret sharing scheme (LSSS). Starting with known ideal constructions, we then propose a modified scheme with improved multiplication ...

This paper deals with two different asymptotically fast algorithms for the computation of ideal sums in quadratic orders. If the class number of the quadratic number field is equal to 1, these algorithms can be used to calculate the GCD in the quadratic order. We show that the calculation of an ideal sum in a fixed quadratic order can be done as fast as in Z up to a constant factor, i.e., in O(...