Foundations of Module and Ring Theory
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POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES
The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...
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A four port network adder-subtractor module, for surface plasmon polariton (SPP) waves based on a ring resonator filter is proposed. The functionality of module is achieved by the phase difference manipulation of guided SPPs through different arms connected to the ring resonator. The module is designed using the concepts of a basic two-port device proposed in this paper. It is shown that two po...
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In [2] the notion of “uniformly ideal” was introduced and developed the basic theory. In this article we introduce and advance a theory which, in a sense, dual to that i.e, the notion of “uniformly secondary module”.
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This article addresses some foundational issues that arise in the study of linear codes defined over finite rings. Linear coding theory is particularly well-behaved over finite Frobenius rings. This follows from the fact that the character module of a finite ring is free if and only if the ring is Frobenius.
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Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...
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