TY - JOUR

T1 - Decompositions of Quotient Rings and m-Power Commuting Maps

AU - Chen, Chih Whi

AU - Koşan, M. Tamer

AU - Lee, Tsiu Kwen

N1 - Funding Information:
Part of the work was carried out when the third author was visiting Gebze Institute of Technology sponsored by TUBITAK (Turkey). He gratefully acknowledges the support from TUBITAK and kind hospitality from the host university. The third author of the work was supported by NSC and NCTS/TPE of Taiwan.

PY - 2013/5

Y1 - 2013/5

N2 - Let R be a semiprime ring with symmetric Martindale quotient ring Q, n ≥ 2 and let f(X) = Xn h(X), where h(X) is a polynomial over the ring of integers with h(0) = ±1. Then there is a ring decomposition Q = Q1 ⊕ Q2 ⊕ Q3 such that Q1 is a ring satisfying S2n-2, the standard identity of degree 2n - 2, Q2 ≅ Mn(E) for some commutative regular self-injective ring E such that, for some fixed q > 1, xq = x for all x ∈ E, and Q3 is a both faithful S2n-2-free and faithful f-free ring. Applying the theorem, we characterize m-power commuting maps, which are defined by linear generalized differential polynomials, on a semiprime ring.

AB - Let R be a semiprime ring with symmetric Martindale quotient ring Q, n ≥ 2 and let f(X) = Xn h(X), where h(X) is a polynomial over the ring of integers with h(0) = ±1. Then there is a ring decomposition Q = Q1 ⊕ Q2 ⊕ Q3 such that Q1 is a ring satisfying S2n-2, the standard identity of degree 2n - 2, Q2 ≅ Mn(E) for some commutative regular self-injective ring E such that, for some fixed q > 1, xq = x for all x ∈ E, and Q3 is a both faithful S2n-2-free and faithful f-free ring. Applying the theorem, we characterize m-power commuting maps, which are defined by linear generalized differential polynomials, on a semiprime ring.

KW - Derivation

KW - Faithful f-free ring

KW - Linear differential polynomial

KW - m-Power commuting map

KW - Semiprime ring

KW - Symmetric Martindale quotient ring

UR - http://www.scopus.com/inward/record.url?scp=84878140906&partnerID=8YFLogxK

U2 - 10.1080/00927872.2011.651764

DO - 10.1080/00927872.2011.651764

M3 - 期刊論文

AN - SCOPUS:84878140906

VL - 41

SP - 1865

EP - 1871

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 5

ER -