On n-Amitsur Rings
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The concepts of an Amitsur ring and a hereditary Amitsur ring, which were introduced and studied by S. Tumurbat in a recent paper, are generalized. For a positive integer n, a ring A is said to be an n-Amitsur ring if γ(A[Xn]) = (γ(A[Xn]) ∩ A)[Xn] for all radicals γ, where A[Xn] is the polynomial ring over A in n commuting indeterminates. If a ring A satisfies the above equation for all hereditary radicals γ, then A is said to be a hereditary n-Amitsur ring. Characterizations and examples of these rings are provided. Moreover, new radicals associated with n-Amitsur rings are introduced and studied. One of these is a special radical and its semisimple class is polynomially extensible.
Abstract
The concepts of an Amitsur ring and a hereditary Amitsur ring, which were introduced and studied by S. Tumurbat in a recent paper, are generalized. For a positive integer n, a ring A is said to be an n-Amitsur ring if γ(A[Xn]) = (γ(A[Xn]) ∩ A)[Xn] for all radicals γ, where A[Xn] is the polynomial ring over A in n commuting indeterminates. If a ring A satisfies the above equation for all hereditary radicals γ, then A is said to be a hereditary n-Amitsur ring. Characterizations and examples of these rings are provided. Moreover, new radicals associated with n-Amitsur rings are introduced and studied. One of these is a special radical and its semisimple class is polynomially extensible.
참고문헌 (14)
- N. Divinsky, "Kurosh radicals of rings with operators", Canad. J. Math, 17, pp.278~280 (1965)
- H. France-Jackson, "On α-like radicals of rings", Bull. Aust. Math. Soc, 88(2), pp.331~339 (2013)
- B. J. Gardner, "Open problems in radical theory", Algebra Discrete Math., (3), pp.15~17 (2007)
- B. J. Gardner, "Radical theory of rings" (2004), Marcel Dekker
- B. J. Gardner, "Small and large radical classes", Comm. Algebra, 20, pp.2533~2551 (1992)
- J. Krempa, "On radical properties of polynomial rings", Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 20, pp.545~548 (1972)
- N. V. Loi, "On the Amitsur property of radicals", Algebra Discrete Math., (3), pp.92~100 (2006)
- N. R. McConnell, "Theory of radicals" (1993), North-Holland
- S. Tumurbat, "On Amitsur rings", Quaest. Math, 42(5), pp.665~672 (2019)
- Sodnomkhorloo Tumurbat, "Notes on Chain Rings and Radicals", Kyungpook Mathematical Journal, 58(3), pp.473~479 (2018), 경북대학교 자연과학대학 수학과
- S. Tumurbat, "Radicals of polynomial rings", Soochow J. Math, 29(4), pp.425~434 (2003)
- S. Tumurbat, "On radicals with Amitsur property", 32(3), pp.1219~1227 (2004)
- S. Tumurbat, "Radicals with the α-Amitsur property", J. Algebra Appl, 7(3), pp.347~361 (2008)
- R. Wiegandt, "Radical and semisimple classes of rings" (1974), Queen’s University