A Problem on Universal Modules

Self Cite

Let k be an algebraically closed field of characteristic zero, and R / I and S / J be algebras over k . Ω 1 ( R / I ) and Ω 1 ( S / J ) denote universal module of first order derivation over k . The main result of this paper asserts that the first nonzero Fitting ideal Ω 1 ( R / I ⊗ k S / J ) is an invertible ideal, if the first nonzero Fitting ideals Ω 1 ( R / I ) and Ω 1 ( S / J ) are invertible ideals. Then using this result, we conclude that the projective dimension of Ω 1 ( R / I ⊗ k S / J ) is less than or equal to one.

Section: Resultsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

On Fitting Ideals of Kahler Differential Module

Turan

Olgun

2018

Self Cite

“…Then, Erdogan studied universal modules of higher differential operators in 1993 [8]. The exterior and symmetric derivations of universal modules were also studied by Osborn [4], Hart [9,10], Erdogan [8], Olgun [11], Merkepçi and Olgun [12], Merkepçi and et al [13], M.E. Sweedler [14] and Karakuş and et al [15].…”

Section: Mathematical Backgroundmentioning

confidence: 99%

On Connection between Second-Degree Exterior and Symmetric Derivations of Kähler Modules

Merkepci

2018

Mathematical physics looks for ways to apply mathematical ideas to problems in physics. In differential forms, the tensor form is first defined, and the definitions of exterior and symmetric differential forms are made accordingly. For instance, M is an R-module, M ⊗ R M the tensor product of M with itself and H a submodule of M ⊗ R M generated by x ⊗ y − y ⊗ x , where x , y in M. Then, ∨ 2 ( M ) = M ⊗ R M / H is called the second symmetric power of M. A role of the exterior differential forms in field theory is related to the conservation laws for physical fields, etc. In this study, I present a new approach to emphasize the properties of second exterior and symmetric derivations on Kahler modules, and I find a connection between them. I constitute exact sequences of ∨ 2 ( Ω 1 ( S ) ) and Λ 2 ( Ω 1 ( S ) ) , and I describe and prove a new isomorphism in the following: Let S be an affine algebra presented by R / I , where R = k [ x 1 , … x s ] is a polynomial algebra and I = ( f 1 , … f m ) an ideal of R. Then, I have J 1 Ω 1 ( S ) ≃ Ω 1 ( S ) ⊕ ∨ 2 ( Ω 1 ( S ) ) ⊕ Λ 2 ( Ω 1 ( S ) .

“…Sahin, Olgun, and Uluçay [16] defined normed quotient rings whileŞahin and Kargın [17] presented neutrosophic triplet normed space. In Reference [18], Olgun andŞahin investigated fitting ideals of the universal module and while Olgun [19] found a method to solve a problem on universal modules. Sahin and Kargin proposed neutrosophic triplet inner product [20] and Florentin,Şahin, and Kargin introduced neutrosophic triplet G-module [21].Şahin and et al defined isomorphism theorems for soft G-module in [22].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Normed Rings

Emniyet

Şahin

2018

In this paper, the concept of fuzzy normed ring is introduced and some basic properties related to it are established. Our definition of normed rings on fuzzy sets leads to a new structure, which we call a fuzzy normed ring. We define fuzzy normed ring homomorphism, fuzzy normed subring, fuzzy normed ideal, fuzzy normed prime ideal, and fuzzy normed maximal ideal of a normed ring, respectively. We show some algebraic properties of normed ring theory on fuzzy sets, prove theorems, and give relevant examples.