TY - JOUR

T1 - Self-free modules and E-rings

AU - Dugas, Manfred

AU - Feigelstock, Shalom

PY - 2003/3/1

Y1 - 2003/3/1

N2 - We call an S -module M self-free with basis X if X is a subset of M and each function f : X → M extends to a unique endomorphism φ : M → M. Such structures were called minimally |X| -free in Bankston and Schutt (Bankston, P., Schutt, R. (1995). On minimally free algebras. Can. J. Math. 37(5):963-978.). If |X| = 1, then M is an E-module over S. We show that if M is slender, then M is a direct sum of |X| many copies of an E-module, without restrictions on the cardinality of X. We also investigate additive groups of torsion-free rings of finite rank without zero-divisors. We find criteria under which these rings are E-rings. Also, we find conditions for abelian groups to be E-groups.

AB - We call an S -module M self-free with basis X if X is a subset of M and each function f : X → M extends to a unique endomorphism φ : M → M. Such structures were called minimally |X| -free in Bankston and Schutt (Bankston, P., Schutt, R. (1995). On minimally free algebras. Can. J. Math. 37(5):963-978.). If |X| = 1, then M is an E-module over S. We show that if M is slender, then M is a direct sum of |X| many copies of an E-module, without restrictions on the cardinality of X. We also investigate additive groups of torsion-free rings of finite rank without zero-divisors. We find criteria under which these rings are E-rings. Also, we find conditions for abelian groups to be E-groups.

KW - E-rings

KW - Self-free modules

UR - http://www.scopus.com/inward/record.url?scp=0037367860&partnerID=8YFLogxK

U2 - 10.1081/AGB-120017772

DO - 10.1081/AGB-120017772

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AN - SCOPUS:0037367860

SN - 0092-7872

VL - 31

SP - 1387

EP - 1402

JO - Communications in Algebra

JF - Communications in Algebra

IS - 3

ER -