The Relationship Between Some Kinds of Ideal in The Order

Abstract

The Relationship Between Some Kinds of Ideal in The Order

Abstract

This work will discuss one of the structures in Mathematics Algebra, namely Order. Simply put, order is a ring that certain criteria. For R is a ring which is of order, defining the R-ideal is difference with defining ideal (regular) in R as it is known in general. An R-ideal in R is certainly an ideal (regular) in R. However, in general, an ideal (regular) in R is not an R-ideal in R. However, in certain circumstances, the ideal (regular) in R is also an R-ideal. In addition to R-ideal, in order also known notion some other ideal. In this paper will be discussed the relationship between several types of ideal in the order

Keywords

• ideal,invertible,order,reflexive,quotient ring

References

1. P. Cohn, Free Ideal Rings and Localization in General Rings, Cambridge University Press, Cambridge, 2006.
2. K.R. Goodearl dan R.B. Warfield, An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, Cambridge, 1989.
3. H. Marubayashi, H. Miyamoto, dan A. Ueda, Non-Commutative Valuation Rings and Semi-Hereditary Orders, Kluwer Academic Publishers, Dordrecht, 1997.
4. J.C. McConnell dan J.C. Robson, Noncommutative Noetherian Rings. John Wiley and Sons, Inc., New York, 1987.
5. O. Zariski dan P. Samuel, Commutative Algebra, D. Van Nostrand Company, Inc. Princeton, 1958.