A Jacobson Radical Decomposition of the Fano-Snowflake Configuration

A Jacobson Radical Decomposition of the Fano-Snowflake Configuration

The Fano-Snowflake, a specific configuration associated with the smallest ring of ternions R♦ (arXiv:0803.4436 and arXiv:0806.3153), admits an interesting partitioning with respect to the Jacobson radical of R♦. The totality of 21 free cyclic submodules generated by non-unimodular vectors of the free left R♦-module R ♦ is shown to split into three disjoint sets of cardinalities 9, 9 and 3 accor...

On Jacobson Radical of a Γ−semiring

We introduce the notions of Jacobson radical of a Γ−semiring and semisimple Γ−semiring and characterize them via operator semirings. AMS Mathematics Subject Classification (2000): 16Y60, 16Y99, 20N10

"Snowflake" divertor configuration in NSTX

Rings and Algebras the Jacobson Radical of a Semiring

The concept of the Jacobson radical of a ring is generalized to semirings. A semiring is a system consisting of a set S together with two binary operations, called addition and multiplication, which forms a semigroup relative to addition, a semigroup relative to multiplication, and the right and left distributive laws hold. The additive semigroup of S is assumed to be commutative. The right ide...

On the Nilpotency of the Jacobson Radical of Semigroup Rings

Munn [11] proved that the Jacobson radical of a commutative semigroup ring is nil provided that the radical of the coefficient ring is nil. This was generalized, for semigroup algebras satisfying polynomial identities, by Okniński [14] (cf. [15, Chapter 21]), and for semigroup rings of commutative semigroups with Noetherian rings of coefficients, by Jespers [4]. It would be interesting to obtai...