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Let $R$ be an associative unital ring and let $a \in R$ be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.

Note sur la méthode d'élimination de Bezout

L. Painvin (1874)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Notes on commutative parasemifields

Vítězslav Kala, Tomáš Kepka, Miroslav Korbelář (2009)

Commentationes Mathematicae Universitatis Carolinae

Parasemifields (i.e., commutative semirings whose multiplicative semigroups are groups) are considered in more detail. We show that if a parasemifield $S$ contains $ℚ^{+}$ as a subparasemifield and is generated by $ℚ^{+} \cup {a}$ , $a \in S$ , as a semiring, then $S$ is (as a semiring) not finitely generated.

If $R$ is a prime ring such that $R$ is not completely reducible and the additive group $R (+)$ is not complete, then $R$ is slender.

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Normalizing extensions of semiprime rings.

Normalizing the cyclic modules of Connes.

Norms on semirings. I.

Note on Categories of Indecomposable Modules

Note on isomorphism theorems of hyperrings.

Note on pure-projectivity of modules

Note on strongly nil clean elements in rings

Note sur la méthode d'élimination de Bezout

Notes on commutative parasemifields

Notes on Galois extensions with inner Galois groups.

Notes on generalized prime and coprime modules. I.

Notes on generalized prime and coprime modules. II.

Notes on generalized $(σ, τ)$ –derivation

Notes on purities

Notes on radical filters of ideals

Notes on slender prime rings

Notes on Whitehead space of an algebra.

Notes on $(α, β)$ -derivations.

Numérateurs et dénominateurs dans le corps de fractions d'un semifir

Currently displaying 81 – 99 of 99