SUBRING Meaning and
Definition
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A subring is a mathematical term used to describe a certain type of structure within the field of algebra. It refers to a subset of a ring that is itself a ring. In simpler terms, it is a smaller ring that is contained within a larger ring.
To be considered a subring, the subset must satisfy several conditions. First, it must be closed under addition. This means that if two elements of the subring are added together, the result must also be an element of the subring. Similarly, the subring must also be closed under multiplication. If two elements are multiplied together, the product must belong to the subring as well.
Additionally, a subring must contain the additive and multiplicative identities of the larger ring, and it must be closed under additive inverses. This means that for every element in the subring, its additive inverse (the element that, when added to it, yields the additive identity) must also be part of the subring.
By having these properties, a subring inherits many of the same algebraic properties as the larger ring. It allows for the study of more specific structures within rings, and provides a framework for exploring their properties and relationships. The concept of a subring is fundamental in abstract algebra and is utilized in various mathematical fields such as number theory, cryptography, and algebraic geometry.
Common Misspellings for SUBRING
- aubring
- zubring
- xubring
- eubring
- wubring
- sybring
- shbring
- sjbring
- s8bring
- s7bring
- suvring
- sunring
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- subeing
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- sub5ing
- sub4ing
- subrung
- subrjng
- subrkng
Etymology of SUBRING
The word "subring" is constructed by combining the prefix "sub-" with the word "ring".
The prefix "sub-" is derived from the Latin preposition "sub", which means "under" or "below". It often indicates a position that is lower, smaller, or subordinate to something else.
The word "ring" comes from the Old English word "hring", which referred to a circular band or object. In mathematics, a ring is a specific algebraic structure that consists of a set of elements equipped with two operations, addition and multiplication, which follow specific axioms and properties.
Therefore, the term "subring" refers to a mathematical concept where a subset of elements in a given ring form a smaller ring itself. It denotes a ring that is "under" or "below" (in terms of size or structure) another ring.
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