Here we study the maximal dimension of the annihilator ideals 0 :A m j of artinian graded rings A = P/(I, x1, x 2 2, . . . , x 2 v) with a given Hilbert function, where P is the polynomial ring in the variables x1, x2, . . . , xv over a field K with each deg xi = 1, I is a graded ideal of P , and m is the graded maximal ideal of A. As an application to combinatorics, we introduce the notion of ...

in this paper, we introduce a new generalization of weakly prime ideals called $i$-prime. suppose $r$ is a commutative ring with identity and $i$ a fixed ideal of $r$. a proper ideal $p$ of $r$ is $i$-prime if for $a, b in r$ with $ab in p-ip$ implies either $a in p$ or $b in p$. we give some characterizations of $i$-prime ideals and study some of its properties.  moreover, we give conditions  ...

For P a poset or lattice, let Id(P ) denote the poset, respectively, lattice, of upward directed downsets in P, including the empty set, and let id(P ) = Id(P )−{∅}. This note obtains various results to the effect that Id(P ) is always, and id(P ) often, “essentially larger” than P. In the first vein, we find that a poset P admits no <-respecting map (and so in particular, no one-to-one isotone...

This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is given. In the case of an ideal lattice of a lattice L, the decomposition into subdirectly irreducib...

Abstract Let G G be a group and R R -graded commutative ring with nonzero unity 1. In this article, we introduce the concept of graded weakly 1-absorbing primary ideals which is generalization ideal. A proper ideal P P said to if whenever nonunit elements x , y<...

We present a setting for the study of torsion theories in general categories. The idea is to associate, with any pair ($\mathcal T$, $\mathcal F$) full replete subcategories category C$, corresponding subcategory Z = \mathcal T \cap F$ \emph{trivial objects} C$. morphisms which factor through Z$ are called Z$-trivial, and these form an ideal morphisms, respect one can define Z$-prekernels, Z$-p...

Gelişen teknolojinin içinde dünyaya gelen Z kuşağı, öncülük ettiği değişimi yaşamın bir parçası olarak algılamış ve hayatı da bu yönde şekillenmiştir. İnternetin yaygınlaşmasıyla birlikte bilgiye ulaşma imkânları geliştiği için kendilerini çok yönlü geliştirme fırsatı bulan kuşak özellikle sosyal medya aracılığıyla haberleşme organize olma becerisine sahiptir. Literatürde yaygın 2000’li yılları...

Proof. (i) We have (1− ζ pn)/(1− ζpn) = 1+ ζpn + · · ·+ ζ i−1 p ∈ Z[ζpn ]. On the other hand, if ii ≡ 1 (mod p), we have (1 − ζpn)/(1 − ζ i pn) = (1 − ζ ii′ pn)/(1 − ζ i pn) = 1 + ζ p + · · ·+ ζ i(i′−1) p ∈ Z[ζpn ], so we find that (1 − ζ i pn) and (1− ζpn) divide one another in Z[ζpn] and hence in OQ(ζpn). (ii) By (i), 1 + ζpn = (1− ζ 2 pn)/(1− ζpn) is a unit in Z[ζpn ], hence in OQ(ζpn). (iii...

The purpose of this paper is to obtain the structure of certain near-rings satisfying the following conditions: (i) d(I) ⊆ Z(N), (ii) d(−I) ⊆ Z(N), (iii) d([x, y]) = 0, (iv) d([x, y]) = [x, y], (v) d(x ◦ y) = 0, (vi) d(x ◦ y) = x ◦ y for all x, y ∈ I , with I is a semigroup ideal and d is a semiderivation associated with an automorphism. Furthermore; an example is given to illustrate that the 3...

We consider the complexity of computing the determinant over arbitrary finite-dimensional algebras. We first consider the case that A is fixed. We obtain the following dichotomy: If A/ radA is noncommutative, then computing the determinant over A is hard. “Hard” here means #P-hard over fields of characteristic 0 and ModpP-hard over fields of characteristic p > 0. If A/ radA is commutative and t...