The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.

EL–hyperstructures are hyperstructures constructed from singlevalued quasi-ordered semigroups. For some kinds of sets it is difficult to find a meaningful single-valued associative operation which could be used as a basis for constructing the EL–hyperstructure. In this paper we use the systematic approach to define it. We focus on multicomponent sets and briefly mention the n–ary context of the...

Some basic algebraic features of quasiparticle transformations are reviewed. Special nonlinear quasiparticle transformations are introduced leading to the second quantized counterparts of gerninal-type (correlated) wave functions. Algebraic representa-' tions of strong and weak orthogonality are discussed, and these issues are generalized to the case of non-orthogonal basis sets leading to the ...

This paper studies the impact of intermediaries’ disappearance on firms’ access to sterling money market during first globalization era 1880-1914. We propose a new methodology assess substitutability in financial networks featuring higher-order structures (credit intermediation chains). represent network as hyperstructure and each credit chain hyperedge. approach allows us how failure intermedi...

Adhesive high-level replacement (HLR) system have been recently introduced as a new categorical framework for graph transformation in the double pushout approach [1, 2]. They combine the well-known framework of HLR systems with the framework of adhesive categories introduced by Lack and Sobociński [3, 4]. The main concept behind adhesive categories are the so-called van Kampen squares, which en...

If D is C+ or D , then we prove that H1(D) is a Hermite regular coherent ring of weak global dimension 2 (the coherence was already proved in [4]). We show: there is a one-to-one equivalence between systems de ned by matrices with entries in H1(D) and coherent H1(D)-modules, coherent H1(D)-modules are stable by elementary algebraic operations, and thus, we can characterize the algebraic propert...

We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-...