Let R be an integral domain and let Q denote the quotient field of R. We investigate the structure of R-submodules of Q that are Q-irreducible, or completely Q-irreducible. One of our goals is to describe the integral domains that admit a completely Q-irreducible ideal, or a nonzero Q-irreducible ideal. If R has a nonzero finitely generated Q-irreducible ideal, then R is quasilocal. If R is int...

Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F ⊆ P (X) of size c, consisting of Borel sets which are not in I . Condition (M) states that there is a Borel function f : X → X with f[{x}] / ∈ ...

let $r$ be a commutative ring with identity and $mathbb{a}(r)$ be the set   of ideals of $r$ with non-zero annihilators. in this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $r$, denoted by $mathbb{ag}_p(r)$. it is a (undirected) graph with vertices $mathbb{a}_p(r)=mathbb{a}(r)cap mathbb{p}(r)setminus {(0)}$, where   $mathbb{p}(r)$ is...

INTRODUCTION Educational justice is a process by which all those involved in education are pondering and seeking to establish it in their regulatory environments. This study aimed to investigate effective factors in an ideal educational justice and the current condition of educational justice from the students' viewpoint and ultimately increase the awareness and understanding of authorities and...

We give a simple sufficient condition for a spun-normal surface in an ideal triangulation to be incompressible, namely that it is a vertex surface with nonempty boundary which has a quadrilateral in each tetrahedron. While this condition is far from being necessary, it is powerful enough to give two new results: the existence of alternating knots with noninteger boundary slopes, and a proof of ...

In this paper, we propose a new precoding method for intersymbol interference (ISI) cancellation by using nonmaximally decimated multirate filterbanks. Unlike the existing precoding methods, such as the TH and trellis precodings, the new precoding i) may be independent of the ISI channel; ii) is linear and does not have to implement any modulo operation; iii) gives the ideal FIR equalization at...

In secret sharing, the exact characterization of ideal access structures is a longstanding open problem. Brickell and Davenport (J. of Cryptology, 1991) proved that ideal access structures are induced by matroids. Subsequently, ideal access structures and access structures induced by matroids have attracted a lot of attention. Due to the difficulty of finding general results, the characterizati...