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The Structure of Local Rings with Singleton Basis and Their Enumeration
Mathematics, 2022 A local ring is an associative ring with unique maximal ideal. We associate with each Artinian local ring with singleton basis four invariants (positive integers) p,n,s,t.
Yousef Alkhamees, Sami Alabiad
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Semihereditary polynomial rings [PDF]
Proceedings of the American Mathematical Society, 1974 It is shown that if the ring of polynomials over a commutative ring R R is semihereditary then R R is von Neumann regular. This is the converse of a theorem of P. J. McCarthy.
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An extension of the reflexive property of rings
Arab Journal of Mathematical Sciences, 2019 Mason introduced the notion of reflexive property of rings as a generalization of reduced rings. For a ring endomorphism α, Krempa studied α-rigid rings as an extension of reduced rings. In this note, we introduce the notion of α-quasi reflexive rings as
Arnab Bhattacharjee
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Design approach for optimization of a piston ring profile considering mixed lubrication
Friction, 2016 To reduce the friction of a piston ring while maintaining a large oil film load-carrying capacity, an approach comprising of the inverse method and the sequential quadratic programming algorithm was proposed. The approach considers the variation of mixed
Zhinan Zhang, Jun Liu, Youbai Xie
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PRESIMPLIFIABLE AND WEAKLY PRESIMPLIFIABLE RINGS
Barekeng, 2023 Let be a commutative ring with identity. Two elements and b in are called to be associates if and , or equivalently, if . The generalization of associate relation in R has given the idea for definitions of presimplifiable and weakly presimplifiable
Deby Anastasya, Sri Wahyuni
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Polynomial Rings over Pseudovaluation Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 LetRbe a ring. Letσbe an automorphism ofR. We define aσ-divided ring and prove the following. (1) LetRbe a commutative pseudovaluation ring such thatx∉Pfor anyP∈Spec(R[x,σ]). ThenR[x,σ]is also a pseudovaluation ring. (2) LetRbe aσ-divided ring such thatx∉Pfor anyP∈Spec(R[x,σ]). ThenR[x,σ]is also aσ-divided ring.
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Graded radical W type Lie algebras I
International Journal of Mathematics and Mathematical Sciences, 2002 We get a new ℤ-graded Witt type simple Lie algebra using a generalized polynomial ring which is the radical extension of the polynomial ring F[x] with the exponential function ex.
Ki-Bong Nam
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N $$ \mathcal{N} $$ = 4 SYM, (super)-polynomial rings and emergent quantum mechanical symmetries
Journal of High Energy Physics, 2023 The structure of half-BPS representations of psu(2, 2|4) leads to the definition of a super-polynomial ring R $$ \mathcal{R} $$ (8|8) which admits a realisation of psu(2, 2|4) in terms of differential operators on the super-ring.
Robert de Mello Koch, Sanjaye Ramgoolam
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Bernoulli-type Relations in Some Noncommutative Polynomial Ring [PDF]
, 2009 We find particular relations which we call "Bernoulli-type" in some noncommutative polynomial ring with a single nontrivial relation. More precisely, our ring is isomorphic to the universal enveloping algebra of a two-dimensional non-abelian Lie algebra.
Murata, Shunsuke
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Polynomial Rings over Goldie Rings
Journal of Algebra, 2001 The authors construct for each finite field \(K\) a commutative Goldie \(K\)-algebra \(R\) such that the polynomial ring \(R[X]\) is not a Goldie ring.
Antoine, Ramon, Cedó, Ferran
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