In this paper we consider algebras with involution over a ring C which is given by the quadratic extension by i of an ordered ring R. We discuss the -representation theory of such -algebras on pre-Hilbert spaces over C and develop the notions of Rieffel induction and formal Morita equivalence for this category analogously to the situation for C-algebras. Throughout this paper the notion of posi...

Abstract In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to subclass algebras, which is called filiform. Note that set filiform algebras fixed dimension can be decomposed into three disjoint families. describe pre-derivations for first and second families determine those in two classes are nilpotent.

The aim of this work is to introduce and study the notions Hom-pre-Jordan algebra Hom-J-dendriform which generalize Hom-Jordan algebras. algebras are regarded as underlying algebraic structures behind Rota-Baxter operators O-operators introduced in paper. also analogues Hom-pre-Lie for anti-commutator a left multiplication operator gives representation algebra. On other hand, analogue Hom-dendr...

Originating from automated theorem proving, deduction modulo removes computational arguments from proofs by interleaving rewriting with the deduction process. From a proof-theoretic point of view, deduction modulo defines a generic notion of cut that applies to any first-order theory presented as a rewrite system. In such a setting, one can prove cut-elimination theorems that apply to many theo...

Associating to each pre-order on the indices 1; :::;n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n n matrix rings. Rings within the order-convex hull of the embedding, i.e. matrix rings that contain the ring of diagonal matrices, can be viewed as incidence algebras of ideal-valued, generalized pre-order relation...

since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

Decision-making is a crucial aspect of emergency response during mass casualty incidents (MCIs). MCIs require rapid decisions to be taken by geographically-dispersed teams in an environment characterized by insufficient information, ineffective collaboration and inadequate resources. Despite the increasing adoption of decision support systems in healthcare, there is limited evidence of their va...