# The five letter word

I will absorb everything, in some of your jewelries.

People call me the highest, only to some proper me.

Modulo by the highest me, there are so few trees.

Modulo by me being 2357, there is decimal number 383.

What am I?

You are

an IDEAL,

which is indeed a five-letter word as the title says.

I will absorb everything, in some of your jewelries.

The definition of an ideal is a subset of a ring ("jewellery") such that when multiplied by any element of the ring, it remains the same set ("absorbing").

People call me the highest, only to some proper me.

A maximal ideal is the largest possible proper ideal within the ring.

Modulo by the highest me, there are so few trees.

The quotient of a ring by its maximal ideal is a field.

Modulo by me being 2357, there is decimal number 383.

The quotient of a ring by a prime ideal (2, 3, 5, 7 being primes) is an integral domain (which probably connects to 383 in some way?)

• Correct! Great job. Commented Dec 19, 2019 at 21:01
• For the 383, rot13(Vg ersref gb gur vagrteny flzoby nf va vagrtengvba, juvpu vf n fgergpurq F, urapr "ybat F", erfhygvat va havpbqr punenpgre H+017S. (Qrpvzny cbvag 383)) Too much wordplay, huh? Commented Dec 19, 2019 at 21:04
• @DannyuNDos Ahaaa, I should have thought of that. Good one. Commented Dec 20, 2019 at 7:15