Let $$L_n$$ be a line graph with n edges and $${{\mathcal {F}}}(L_n)$$ the facet ideal of its matching complex. In this paper, we provide irreducible decomposition some exact formulas for projective dimension regularity .

We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty. We are concerned with the following question: Which algebras are homomorphic images of subdirectly irreducible algebras? A necessary condition, discovered...

Characterizations of fuzzy ideals of a pseudo-BCH-algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. The homomorphic properties of fuzzy ideals are provided. Finally, characterizations of Noetherian pseudo-BCH-algebras and Artinian pseudoBCH-algebras via fuzzy ideals are obtained. Mathematics Subject Classi…cation: 03G25, 06F35.

This paper investigates the arithmetic of fractional ideals and the infrastructure of the principal ideal class of a purely cubic function eld of unit rank one. We rst describe how irreducible polynomials split into prime ideals in purely cubic function elds of nonzero unit rank. This decomposition behavior is used to compute so-called canonical bases of fractional ideals; such bases are very s...

We introduce the concept of topological finite-determinacy for germs analytic functions within a fixed ideal I, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We generalize classical results of Thom and Varchenko stating the following: let A be the complement in the ideal I of the space of germs whose topological type remains unchanged un...

We prove a Dirichlet theorem for polynomial rings: Let F be a pseudo algebraically closed field (i.e., each nonempty variety defined over F has an F-rational point). Then for all relatively prime polynomials a(X), b(X) ∈ F [X] and for every sufficiently large integer n there exist infinitely many polynomials c(X) ∈ F [X] such that a(X) + b(X)c(X) is irreducible of degree n, provided that F has ...

Let ` → −∞. Recent developments in convex calculus [26] have raised the question of whether E = א0. We show that every closed, meager subalgebra is Y -unconditionally Darboux, combinatorially pseudo-Chern and ultra-almost surely Euclidean. It is well known that every irreducible, onto, right-canonical isometry is integrable, reversible, K-trivially universal and Dedekind. It has long been known...

In this paper, we present a characteristic set method for mixed differential and difference polynomial systems. We introduce the concepts of coherent, regular, proper irreducible, and strongly irreducible ascending chains and study their properties. We give an algorithm which can be used to decompose the zero set for a finitely generated differential and difference polynomial sets into the unio...

Maximal length sequences (m-sequences) are also known as pseudo random sequences or pseudo noise sequences for closely following Golomb’s popular randomness properties: (P1) balance, (P2) run, and (P3) ideal autocorrelation. Apart from these, there also exist certain other less known properties of such sequences all of which are discussed in this tutorial paper. Comprehensive proofs to each of ...