In this document we consider the prime spectrum of an MV-algebra with certain natural operations. These are used to show connections between the classes of prime lattice filters and prime implication filters.

In this note, we show how abstract localization and graded versions of the Artin-Rees property may be applied to construct structure sheaves over the projective spectrum Proj(R) of a graded fully bounded noetherian ring R.

If one wants to investigate the properties and relations of homogeneous ideals in a commutative graded ring, one has as a model on the one hand the well known case of a polynomial ring and on the other hand the general commutative ideal theory. The case of a polynomial ring has been studied for the sake of algebraic geometry, and one of the methods was traditionally the passage to nonhomogeneou...

We characterize ring spectra morphisms from the algebraic cobordism spectrum MGL ([12]) to an oriented spectrum E (in the sense of Morel [4]) via formal group laws on the ”topological” subring E∗ = ⊕iE 2i,i of E∗∗. This result is then used to construct for any prime p a motivic Quillen idempotent on MGL(p). This defines the BP -spectrum associated to the prime p as in Quillen’s [6] for the comp...

Let $R$ be an associative ring and let $M$ be a left $R$-module.Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, t...

Let $R$ be a commutative ring with identity and $M$ be an$R$-module. Let $FSpec(M)$ denotes the collection of all prime fuzzysubmodules of $M$. In this regards some basic properties of Zariskitopology on $FSpec(M)$ are investigated. In particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$FSpec(M)$ is a $T_0-$spa...

We calculate the RO(G)-graded coefficients of HZ_, Eilenberg-MacLane spectrum constant Mackey functor for quaternion group Q8.

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...