let $r$ be a commutative ring with identity and $m$ be a unitary$r$-module. the primary-like spectrum $spec_l(m)$ is thecollection of all primary-like submodules $q$ such that $m/q$ is aprimeful $r$-module. here, $m$ is defined to be rsp if $rad(q)$ isa prime submodule for all $qin spec_l(m)$. this class containsthe family of multiplication modules properly. the purpose of thispaper is to intro...

The notion of a subtractive category, recently introduced by the author, is a “categorical version” of the notion of a (pointed) subtractive variety of universal algebras, due to A.Ursini. We show that a subtractive variety C, whose theory contains a unique constant, is abelian (i.e. C is the variety of modules over a fixed ring), if and only if the dual category Cop of C, is subtractive. More ...

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.

Subtractive cloning is a powerful technique for isolating genes expressed or present in one cell population but not in another. This method and a related one termed positive selection have their origins in nucleic acid reassociation techniques. We discuss the history of subtractive techniques, and fundamental information about the nucleic acid composition of cells that came out of reassociation...

A small-scale microphone array generally adopts the subtractive beamforming technique, which constructs sharp notches in a spatial beampattern, so that target sound sources are assumed as point sound sources. However, the shapes of actual sound sources are various and not always points. Our mouths are line sound sources or plane sound sources. It is important to deal with line sound sources whe...

For several semirings S, two weighted finite automata with multiplicities in S are equivalent if and only if they can be connected by a chain of simulations. Such a semiring S is called “proper”. It is known that the Boolean semiring, the semiring of natural numbers, the ring of integers, all finite commutative positively ordered semirings and all fields are proper. The semiring S is Noetherian...

We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule Sn over a semiring S is rational if it has a generating family that is a rational subset of Sn, Sn being thought of as a monoid under the entrywise prod...

We present a formulae-as-types interpretation of Subtractive Logic (i.e. bi-intuitionistic logic). This presentation is two-fold: we first define a very natural restriction of the λμ-calculus which is closed under reduction and whose type system is a constructive restriction of the Classical Natural Deduction. Then we extend this deduction system conservatively to Subtractive Logic. From a comp...