Let $R$ be a commutative ring with identity and $I$ proper ideal of $R$. In this paper we introduce the ideal-based quasi zero divisor graph $Q\Gamma_{I}(R)$ respect to which is an undirected vertex set $V=\{a\in R\backslash\sqrt{I}:$ $ab\in I$ for some $b\in R\backslash\sqrt{I}\}$ two distinct vertices $a$ $b$ are adjacent if only I$. We study basic properties such as diameter, girth, dominato...

In this paper, the author studied skeletal congruences θ^* of a distributive nearlattice S, where * represents pseudocomplement. Then described θ(I)^*, θ(I) is smallest congruence S containing n-ideal I as class and showed that I^+ n-kernel θ(I)^*. established following fundamental results: When n an upper element has shown n-kernels are precisely those n-ideals which intersection relative anni...

Weighted cup-length calculations in singular cohomology led Farber and Grant in 2008 to general lower bounds for the topological complexity of lens spaces. We replace singular cohomology by connective complex K-theory, and weighted cup-length arguments by considerations with biequivariant maps on spheres to improve on Farber–Grant’s bounds by arbitrarily large amounts. Our calculations are base...

We characterize Frobenius algebras A as algebras having a comultiplication which is a map of A-modules. This characterization allows a simple demonstration of the compatibility of Frobenius algebra structure with direct sums. We then classify the indecomposable Frobenius algebras as being either \annihilator algebras" | algebras whose socle is a principal ideal | or eld extensions. The relation...

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...

We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the Irreducibility theorem and Duflo theorem, to much wider classes of algebras. Our general version of Irreducibility theorem says that if A is a positively filtered associative algebra such that grA is a commutative Poisson algebra with finitely many symplectic leaves, then the associated v...

Let K be a field of characteristic 0 and S = K[x1, . . . , xn] the polynomial ring over K with graded maximal ideal m = (x1, . . . , xn). Denote by βi(M) = Tor S i (K,M) the ith Betti number of a finitely generated graded module M and by Gin(I) the generic initial ideal of a graded ideal I with respect to the reverse lexicographical order. In this paper we answer (positively) a question raised ...

We present a new class of graded irreducible representations Leavitt path algebra. This is in the sense that its representation space not isomorphic to any existing simple Chen modules. The corresponding modules complete list which are graded, creating an exhaustive class: annihilator module equal either or this type. Our characterization primitive ideals algebra terms properties underlying gra...