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...

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...

Objectives/Background: The ternary seminear ring is the generalization of and it need not be a semiring. Characterization quotient rings some structures have been analysed also studied ideals in rings. Further quasi defined discussed about their properties. Methods: Properties semiring employed to carry out this research work obtain all characterizations corresponding that Findings: We call an ...

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.

Good and Hughes [9] introduced the notion of bi-ideal and Steinfeld [11, 12] introduced the notion of quasi-ideal. Sioson [10] studied some properties of quasi-ideals of ternary semigroups. In [1], Dixit and Dewan studied about the quasi-ideals and bi-ideals of ternary semigroups. Quasi-ideals are generalization of right ideals, lateral ideals, and left ideals whereas bi-ideals are generalizati...

the concept of right (left) quotient (or residual) of an ideal η by anideal ν of an l-subring μ of a ring r is introduced. the right (left) quotients areshown to be ideals of μ . it is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an l-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . most of the results pertaining to the notion of quotients(or residual) of ...

In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings established in [11] and improved in [4] — such an approach naturally imposing the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. Besides some basic yet fundamental results of more general interest for semiri...

We define the family of n-gram embeddings from strings over a finite alphabet into the semimodule N . We classify all ∈ N that are valid images of strings under such embeddings, as well as all whose inverse image consists of exactly 1 string (we call such uniquely decodable). We prove that for a fixed alphabet, the set of all strings whose image is uniquely decodable is a regular language. © 20...