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articleNo Access
GCD and LCM-like identities for ideals in commutative rings
- D. D. Anderson,
- Shuzo Izumi,
- Yasuo Ohno, and
- Manabu Ozaki
Journal of Algebra and Its Applications07 Sep 2015
Preview Abstract
Let A₁,…,A_n(n ≥ 2) be ideals of a commutative ring R. Let G(k) (resp., L(k)) denote the product of all the sums (resp., intersections) of k of the ideals. Then we have
In the case R is an arithmetical ring we have equality. In the case R is a Prüfer ring, the equality holds if at least n - 1 of the ideals A₁,…,A_n are regular. In these two cases we also have
Related equalities are given for Prüfer v-multiplication domains and formulas relating GCD's and LCM's in a GCD domain generalizing gcd(a₁, a₂)lcm(a₁, a₂) = a₁a₂ are given.
articleNo Access
Characterization of some specific lee distance codes over finite rings
- Shalini Gupta,
- Ashish Bamta, and
- Ashwini Kumar
Discrete Mathematics, Algorithms and Applications26 Jun 2024
Preview Abstract
Codes over integer rings equipped with the Lee metric are gaining attention among researchers recently. In this paper, we investigate some specific linear codes over integer rings and characterize their dimensions and Lee weights using greatest common divisors (GCD). Furthermore, we construct equidistant Lee codes over $ℤ_{2^{b}}, ℤ_{2 p} and ℤ_{p}$ which have applications in error detection and error correction.

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