a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular, a commutative ring is a simple ring if...

Simple aromatic rings, also known as simple arenes or simple aromatics, are aromatic organic compounds that consist only of a conjugated planar ring system...

In chemistry, a ring is an ambiguous term referring either to a simple cycle of atoms and bonds in a molecule or to a connected set of atoms and bonds...

ranging from 35–63 mm (1.4–2.5 in). Designs range from the simple to the complex. Simple rings may lie flat on a surface, while others are ergonomically...

not abelian Some examples of rings that are not typically commutative (but may be commutative in simple cases): The free ring Z ⟨ x 1 , … , x n ⟩ {\displaystyle...

simple and a simple commutative ring is a field. The matrix ring over a skew-field is a simple ring. If f : R → S {\displaystyle f:R\to S} is a ring homomorphism...

(not necessarily commutative) ring is said to be semisimple (or completely reducible) if it is the direct sum of simple (irreducible) submodules. For...

theorem characterizes every simple Artinian ring as a ring of matrices over a division ring. This implies that a simple ring is left Artinian if and only...

center is k and is simple if it is a simple ring. Since the center of a simple k-algebra is a field, any simple k-algebra is a central simple algebra over its...

zero ring is −∞. The zero ring is semisimple but not simple. The zero ring is not a central simple algebra over any field. The total quotient ring of the...

In ring theory, a branch of mathematics, a semisimple algebra is an associative Artinian algebra over a field which has trivial Jacobson radical (only...

commutative) ring. The concept of a module also generalizes the notion of an abelian group, since the abelian groups are exactly the modules over the ring of integers...

integers. Ring theory studies the structure of rings; their representations, or, in different language, modules; special classes of rings (group rings, division...

used rings of various designs reflecting their own tastes. Pius IX's ornate ring contained more than a hundred diamonds; John XXIII's ring was a simple cameo...

known as ring theory, a left primitive ring is a ring which has a faithful simple left module. Well known examples include endomorphism rings of vector...

generalization of both integral domains and simple rings. Although this article discusses the above definition, prime ring may also refer to the minimal non-zero...

(−NH2), at the C6 carbon in adenine and C2 in guanine. Similarly, the simple-ring structure of cytosine, uracil, and thymine is derived of pyrimidine,...

In mathematics, specifically in ring theory, the simple modules over a ring R are the (left or right) modules over R that are non-zero and have no non-zero...

of endomorphisms. The ring Mn(D) over a division ring D is an Artinian simple ring, a special type of semisimple ring. The rings C F M I ( D ) {\displaystyle...

normal subgroup. A ring is called a simple ring if it does not contain a nontrivial two sided ideal. A module is called a simple module if it does not...

assembled wise men to create a ring that will make him happy when he is sad. After deliberation the sages hand him a simple ring with the Persian words "This...

every variety contains a simple algebra. Simple group Simple ring Central simple algebra Lampe, W.A.; Taylor, W. (1982). "Simple algebras in varieties"...

finite rings in their own right has a more recent history. Although rings have more structure than groups do, the theory of finite rings is simpler than...

central simple algebra is a central algebra that is also a simple ring. centralizer 1.  The centralizer of a subset S of a ring is the subring of the ring consisting...

third style is a simple ring, the Tattersall or yearling bit, used alone on a bridle, usually for use in-hand. Today, the Dexter ring bit is the most common...

sense to speak of the quotient ring R / (ker f). The first isomorphism theorem for rings states that this quotient ring is naturally isomorphic to the...

mathematics, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is...

general than a semisimple ring, but where simple modules still provide enough information about the ring. Rings such as the ring of integers are semiprimitive...

the ring of endomorphisms of V is semi-simple. As indicated above, the theory of semi-simple rings is much more easy than the one of general rings. For...

mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates...