Unit sum numbers of ringsAn associa

Unit sum numbers of rings
An associative unital ring R is said to have the n–sum property if every element of R can
be written as the sum of exactly n units of R. It is immediate that if R has the n–sum
property then it has the k–sum property for every k ≥ n. (It might seem more useful
at first sight to confine the n–sum property to the non–zero elements of R. However, by
considering for example the field GF(2) which would have the 1–sum property in this new
sense, one sees that the k–sum property for k ≥ 1 does not hold.) Thus it makes sense to
define the unit sum number of R by usn(R) = min{n | R has the n−sum property}. If
there is an element of R which cannot be written as a sum of units we write usn(R) = ∞;
if every element of R is a sum of units but R does not have the n–sum property for any
integer n, we write usn(R) = ω.

ผลลัพธ์ (อังกฤษ) 2:

Numbers of Rings UNIT Sum
An associative Unital Ring R is said to have the n-Sum Property if every element of R Can
be written as the Sum of exactly n Units of R. It is immediate that if R has the n-Sum
Property then. Has the k-sum property for every k ≥ n. (It Might seem more useful
at First Sight to Confine the n-Sum Property to the non-Zero Elements of R. However, by
considering for example the field GF (2) which would have the 1-Sum Property in this New
Sense,. one sees that the K-Sum Property for K ≥ 1 does not Hold.) Thus it Makes Sense to
define the UNIT Sum Number of R by USN (R) = min {n | R} has the n-Sum Property. If
there is an element of R which Can not be written as a Sum of Units we write USN (R) = ∞;
if every element of R is a Sum of Units but R does not have the n-Sum Property for any
integer n,. we write usn (R) = ω.

ผลลัพธ์ (อังกฤษ) 3:

Unit sum numbers of rings
An associative unital ring R is said to have the N - sum property if every element of R can
be. Written as the sum of exactly n units of R. It is immediate that if R has the N - sum
property then it has the K - sum property. For every k > = n. (It might seem more useful
at first sight to confine the N - sum property to the non - zero elements of R.? However, the by
.Considering for example the field GF (2) which would have the 1 - sum property in this new
sense one sees, that the K - sum. Property for k > = 1 does not hold.) Thus it makes sense to
define the unit sum number of R by USN (R) = min {n | R has the. N − sum property}. If
there is an element of R which cannot be written as a sum of units we write USN (R) = ∞;
.If every element of R is a sum of units but R does not have the N - sum property for any
integer n we write, USN (R) = conductivity.