RESIDUAL OF IDEALS OF AN L-RING

Document Type: Research Paper

Author

ATMA RAM SANATAN DHARMA COLLEGE, UNIVERSITY OF DELHI, DHAULA KUAN, NEW DELHI – 110021, INDIA

Abstract

The concept of right (left) quotient (or residual) of an ideal η by an
ideal ν of an L-subring μ of a ring R is introduced. The right (left) quotients are
shown to be ideals of μ . It is proved that the right quotient [η :r ν ] of an ideal
η by an ideal ν of an L-subring μ is the largest ideal of μ such that
[η :r ν ]ν ⊆ η . Most of the results pertaining to the notion of quotients
(or residual) of an ideal of ordinary rings are extended to L-ideal theory of
L-subrings.

Keywords


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