In this paper we describe a computer program for searching all four-element multiplicatively idempotent semirings. We have established that up to the isomorphism of such semirings exactly 381, they are represented by Cayley tables additive and multiplicative reducts. give necessary definitions, properties illustrations.

Crawley-Boevey and Shaw recently introduced a certain multiplicative analogue of the deformed preprojective algebra, which they called the multiplicative preprojective algebra. In this paper we study the moduli space of (semi)stable representations of such an algebra (the multiplicative quiver variety), which in fact has many similarities to the quiver variety. We show that there exists a compl...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...

Exploring further the connection between exponentiation on real closed fields and existence of an integer part modelling strong fragments arithmetic, we demonstrate that each model true arithmetic is exponential field elementarily equivalent to numbers with Peano a admits isomorphism its ordered additive multiplicative group positive elements. Under assumption Schanuel’s Conjecture, obtain stre...

Our goal will be to find subsets of Zm that form groups under the operation of multiplication modulo m. By utilizing the isomorphism Zm ∼= Zn ⊕ Zk, we will find multiplicative groups contained in Zn ⊕ Zk and then map these back to Zm. In particular, if m = nk with gcd(n, k) = 1, our objective is to find particular multiplicative subsets of Zn × Zk that are groups and whose first coordinate is a...

The purpose of this paper is to study conditions under which the restriction of a certain Galois connection on a complete lattice yields an isomorphism from a set of prime elements to a set of coprime elements. An important part of our study involves the set on which the way-below relation is multiplicative.

The structure of the group of quasi multiplicative arithmetical functions such that f(1) 6=0 with respect to Dirichlet and the more general Davison convolution via an isomorphism to a subgroup of upper triangular and Toeplitz matrices will be described. AMS Classification Number: 11A25

We introduce an extension of continuous wavelet theory that enables efficient implementation multiplicative operators in the coefficient space. In new theory, signal space is embedded a larger abstract – so called window–signal There canonical transform to isometric isomorphism between and Hence, framework wavelet-Plancherel extended transform. Since isomorphism, any operation can be pulled-bac...

The Freud ensemble of random matrices is the unitary invariant corresponding to weight $\exp(-n |x|^{\beta})$, $\beta>0$, on real line. We consider local behaviour eigenvalues near zero, which exhibits a transition in $\beta$. If $\beta\ge 1$, it described by standard sine process. Below critical value $\beta=1$, process depending $\beta$, and we determine first two terms large gap probability ...

Let G be a commutative affine algebraic group over field F, and let H:FieldsF→AbGrps functor. A (homomorphic) H-invariant of is natural transformation Tors(−,G)→H, where Tors(−,G) the functor FieldsF→AbGrps taking extension L/F to isomorphism classes GL-torsors Spec(L). The goal this paper compute Invhom1(G,H) H-invariants when multiplicative type, H L×⊗ZQ/Z.