MATH 436 Notes: Ideals

MATH 436 Notes: Subgroups and Cosets

Some notes on the characterization of two dimensional skew cyclic codes

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

σ-sporadic prime ideals and superficial elements

Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $sigma(I^n)$, which denoted by $Ass(A/sigma(I^n))$, stabilize to $A_{sigma}(I)$. We give some properties of the sets $S^{sigma}_{n}(I)=Ass(A/sigma(I^n))setminus A_{sigma}(I...

MATH 436 Notes: Cyclic groups and Invariant Subgroups

Thus if x has infinite order then the elements in the set {x|k ∈ Z} are all distinct while if x has order o(x) ≥ 1 then x = e exactly when k is a multiple of o(x). Thus x = x whenever m ≡ n modulo o(x). By the First Isomorphism Theorem, < x >∼= Z/o(x)Z. Hence when x has finite order, | < x > | = o(x) and so in the case of a finite group, this order must divide the order of the group G by Lagran...

Generalizing the Borel property

We introduce the notion of Q-Borel ideals: ideals which are closed under the Borel moves arising from a poset Q. We study decompositions and homological properties of these ideals, and offer evidence that they interpolate between Borel ideals and arbitrary monomial ideals.