Results 11 to 20 of about 7,915 (113)
A Comparison of Deformations and Geometric Study of Varieties of Associative Algebras
International Journal of Mathematics and Mathematical Sciences, 2007 The aim of this paper is to give an overview and to compare the different deformation theories of algebraic structures. In each case we describe the corresponding notions of degeneration and rigidity.
Abdenacer Makhlouf
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Commutator automorphisms of formal power series rings [PDF]
Proceedings of the American Mathematical Society, 2005 For a big class of commutative rings R R , every continuous
Gubeladze, Joseph, Mushkudiani, Zaza
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FACTORING POLYNOMIALS IN THE RING OF FORMAL POWER SERIES OVER ℤ [PDF]
International Journal of Number Theory, 2012 We consider polynomials with integer coefficients and discuss their factorization properties in ℤ[[x]], the ring of formal power series over ℤ. We treat polynomials of arbitrary degree and give sufficient conditions for their reducibility as power series.
Birmajer, Daniel +2 more
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Nondegenerate Ideals in Formal Power Series Rings
Rocky Mountain Journal of Mathematics, 2004 Let \(A\) be the formal power series ring \(\mathbb{C}[[x_1,\dots, x_n]]\) over \(\mathbb{C}\). For \(k=(k_1,\dots, k_n)\in \mathbb{Z}^n_+\), put \(x^k= x^{k_1}_1\cdots x^{k_n}_n\) and an element \(g= \sum a_{k_1,\dots, k_n} x^{k_1}_1\cdots x^{k_n}_n\) of \(A\) is written as \(g=\sum a_k x^k\). For an element \(g= \sum a_k x^k\) and an ideal \(I\) of \(
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Formal power series rings over a $\pi$-domain
Journal of the European Mathematical Society, 2009 Let R be an integral domain, Χ be a set of indeterminates over R , and
Kang, BG, Oh, DY
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Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules
Forum of Mathematics, SigmaLet ${\mathscr {G}} $ be a special parahoric group scheme of twisted type over the ring of formal power series over $\mathbb {C}$ , excluding the absolutely special case of $A^{(2)}_{2\ell }$ .
Marc Besson, Jiuzu Hong
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Catenarity of formal power series rings over a pullback
Journal of Pure and Applied Algebra, 1992 Let \((T,M,K)\) be a quasi local domain with maximal ideal \(M\) and residue class field \(K\). If \(\varphi\) is the natural surjection of \(T\) on \(K\), for any subring \(D\) of \(K\), \(\varphi^{-1}(D)=R\) is called the pull back. The main interest of the authors is in finding conditions for \(R[[X_ 1,\dots,X_ n]]\) catenarian.
ANDERSON DF +3 more
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$G$-codes over formal power series rings and finite chain rings
Journal of Algebra Combinatorics Discrete Structures and Applications, 2020 In this work, we define $G$-codes over the infinite ring $R_\infty$ as ideals in the group ring $R_\infty G$. We show that the dual of a $G$-code is again a $G$-code in this setting. We study the projections and lifts of $G$-codes over the finite chain rings and over the formal power series rings respectively.
Steven T. DOUGHERTY +2 more
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On the maximal condition in formal power series rings [PDF]
Colloquium Mathematicum, 1992 Let \(R\) denote a ring with an identity element which satisfies the maximal condition for left ideals: equivalently, every left ideal is finitely generated. We give an indirect proof that the ring of formal power series in \(n\) indeterminates over \(R\) also satisfies the maximal condition for left ideals.
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A fresh look into monoid rings and formal power series rings [PDF]
Journal of Algebra and Its Applications, 2019 In this paper, the ring of polynomials is studied in a systematic way through the theory of monoid rings. As a consequence, this study provides canonical approaches in order to find easy and rigorous proofs and methods for many facts on polynomials and formal power series; some of them as sample are treated in this paper.
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