16 citations · 27 across the 12 of their papers we have counts for
15 papers
On some counterparts of Rickart -algebras
Farhodjon Arzikulov, Utkirbek Khakimov
In the present paper, we introduce and study counterparts of Rickart involutive algebras, i.e., almost inner Rickart algebras. We prove that a nilpotent associative algebra, which…
Local and 2-local derivations on Lie matrix rings over commutative involutive rings
Shavkat Ayupov, Farhodjon Arzikulov, Sardorbek Umrzaqov
In the present paper we prove that every 2-local inner derivation on the Lie ring of skew-adjoint matrices over a commutative -ring is an inner derivation. We also apply our tec…
2-Local and local derivations on Jordan matrix rings over commutative involutive rings
Sh. A. Ayupov, F. N. Arzikulov, N. M. Umrzaqov +1
In the present paper we prove that every 2-local inner derivation on the Jordan ring of self-adjoint matrices over a commutative involutive ring is a derivation. We also apply our…
Conservative algebras of -dimensional algebras, III
Farhodjon Arzikulov, Nodirbek Umrzaqov
In the present paper we prove that every local and -local derivation on conservative algebras of -dimensional algebras are derivations. Also, we prove that every local and $2…
Description of 2-local derivations and automorphisms on finite dimensional Jordan algebras
Shavkat Ayupov, Farhodjon Arzikulov, Nodirbek Umrzaqov +1
In the present paper we introduce and investigate the notion of 2-local linear map on vector spaces. A sufficient condition is obtained for linearity of a 2-local linear map on fin…
Local derivations on associative and Jordan matrix algebras
Sh. Ayupov, F. Arzikulov
In the present paper we prove that every additive (not necessarily homogenous) local inner derivation on the algebra of matrices over an arbitrary field is an inner derivation, and…
Description of 2-local derivations on some Lie rings of skew-adjoint matrices
Shavkat Ayupov, Farhodjon Arzikulov
In the present paper we prove that every 2-local inner derivation on the Lie ring of skew-symmetric matrices over a commutative ring is an inner derivation. We also apply our techn…
Two-Local derivations on associative and Jordan matrix rings over commutative rings
Shavkat Ayupov, Farhodjon Arzikulov
In the present paper we prove that every 2-local inner derivation on the matrix ring over a commutative ring is an inner derivation and every derivation on an associative ring has…
Jordan counterparts of Rickart and Baer -algebras, II
Shavkat Ayupov, Farhodjon Arzikulov
We introduce and investigate new classes of Jordan algebras which are close to but wider than Rickart and Baer Jordan algebras considered in our previous paper. Such Jordan algebra…
Jordan counterparts of Rickart and Baer -algebras
Shavkat Ayupov, Farhodjon Arzikulov
There are Jordan analogues of annihilators in Jordan algebras which are called Jordan annihilators. The present paper is devoted to investigation of those Jordan algebras every Jor…
2-Local derivations on algebras of matrix-valued functions on a compact
Shavkat Ayupov, Farhodjon Arzikulov
In the present paper 2-local derivations on various algebras of infinite dimensional matrix-valued functions on a compact are considered. It is proved that every 2-local derivation…
Reversible AJW-algebras
Shavkat Ayupov, Farhodjon Arzikulov
In this article it is proved that for every special AJW-algebra there exist central projections , , , such that (1) is reversible and there exists…
2-Local derivations on AW-algebras of type I
Shavkat Ayupov, Farkhad Arzikulov
It is proved that every 2-local derivation on an AW-algebra of type I is a derivation. Also an analog of Gleason theorem for signed measures on projections of homogenous AW…
2-Local derivations on matrix rings over associative rings
Shavkat Ayupov, Farhodjon Arzikulov
In the present paper it is proved that every inner 2-local derivation on the matrix ring of matrices over a commutative associative ring is an inner de…
Infinite order decompositions of C-algebras
F. N. Arzikulov
In the given article infinite order decompositions of C-algebras are investigated. We give complete proofs of the following statements: 1) If the order unit space $\sum_{ξ,η}^\…