Equational theories of some linear equations are studied. As a consequence, semimodule representations of the corresponding algebras are obtained. Examples are shown on medial and paramedial equations and some of their general-

We provide an expression for the conductor \(c(\varDelta )\) of a semimodule \(\varDelta \) numerical semigroup \(\varGamma with two generators in terms syzygy module and semigroup. In particular, we deduce that difference between is element \), as well formula dual \).

In recent years ternary reversible logic has gained more attention because of its enormous potential in different fields, in particular quantum computing. In order for any future technologies to be reliable they must be testable, thus developing testing techniques in this area is of great importance. In this work we propose a new approach for creating an online testable ternary reversible circu...

We find sufficient conditions for a subclone C of Burle’s clone and for a subclone of the polynomial clone of a finite semimodule to have the property that the associated C-minor partial order has finite principal ideals. We also prove that for these clones the C-minor partial order is universal for the class of countable partial orders whose principal ideals are finite.

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on...

We determine the cost of performing Shor’s algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault tolerant computing on ternary quantum systems: (i) a model based on magic state distillation that assumes the availability of the ternary Clifford gates, projective measurements, classical control and (ii) a model based on a metaplectic topolo...

In this note we describe conditions under which, in idempotent functional analysis (see [1–3]), linear operators have integral representations in terms of idempotent integral of V. P. Maslov. We define the notion of nuclear idempotent semimodule and describe idempotent analogs of the classical kernel theorems of L. Schwartz and A. Grothendieck (see, e.g., [4–6]). In [11], for the idempotent sem...

in a ternary semihyperring, addition is a hyperoperation and multiplicationis a ternary operation. indeed, the notion of ternary semihyperringsis a generalization of semirings. our main purpose of this paper is to introducethe notions of fuzzy hyperideal and fuzzy bi-hyperideal in ternary semihyperrings.we give some characterizations of fuzzy hyperideals and investigateseveral kinds of them.