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Semigroup Forum, 1985 A ring is called strongly regular if its multiplicative semigroup is inverse. This definition is equivalent to more conventional definitions of strongly regular rings [for example, to a definition given by \textit{R. Arens} and \textit{I. Kaplansky}, Trans. Am. Math. Soc. 63, 457-481 (1948; Zbl 0032.00702)].
Schein, B.M., Li, L.
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EXTENSIONS OF STRONGLY π-REGULAR RINGS [PDF]
Bulletin of the Korean Mathematical Society, 2014 An ideal I of a ring R is strongly π-regular if for any x ∈ I there exist n ∈ N and y ∈ I such that x = xy. We prove that every strongly π-regular ideal of a ring is a B-ideal. An ideal I is periodic provided that for any x ∈ I there exist two distinct m,n ∈ N such that x = x. Furthermore, we prove that an ideal I of a ring R is periodic if and only if
Chen H., Kose H., Kurtulmaz, Y.
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On SSAGP-injective Rings [PDF]
مجلة التربية والعلم, 2019 In this paper, we investigate some properties of rings whose simple singular right R- modules are A Gp-injective (or SSAGP- injective for short). It is proved that: Y(R)=0 where R is a right SSAGP- injective rings.
Raida Mahmood, Manal Abd
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On Rings whose Maximal Ideals are GP-Ideals [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2005 This paper introduces the notion of maximal GP-ideal .We studied the class of rings whose maximal left ideal are right GP-ideal. We call such ring MRGP-rings. We consider a necessary and sufficient condition for MRGP-rings to be MRCP-rings. We also study
Raida Mahmood, Manal Abd
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Strongly Regular Extensions of Rings [PDF]
Nagoya Mathematical Journal, 1962 As defined by Arens and Kaplansky [2] a ring A is strongly regular (s.r.) in case to each a∊ A there corresponds x = xa ∊A depending on a such that a 2 x = a. In the present article a ring A is defined to be a s.r.
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On Completely YJ-injective Rings [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2013 A ring R is called completely right YJ-injective (briefly, right CYJ injective ) if every homomorphic image of R is right YJ-injective. In this paper, we study completely right YJ-injective rings and their connection with Von Neumann regular rings.
Raida Mahammod, Husam Mohammad
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SOME RESULTS ON STRONGLY π-REGULAR RIN
Tikrit Journal of Pure Science, 2023 In this paper we study the strongly - regular ring (for short st. -reg. rg.) and some properties also give some new results of st. -reg. rg. and its connection with other rings.
Sinan O. Al-Salihi, Emad I. Jassim
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On Weakly Regular Rings and SSF-rings [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2006 In this work we consider weakly regular rings whose simple singular right R-Modules are flat. We also consider the condition (*): R satisfies L(a)Ír(a) for any aÎR. We prove that if R satisfies(*) and whose simple singular right R-module are flat, then Z
Raida Mahmood
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On strongly regular near-rings [PDF]
Proceedings of the Edinburgh Mathematical Society, 1984 According to Mason [1] a right near-ring N is called (i) left (right) strongly regular if for every a there is an x in N such that a = xa2 (a = a2x) and (ii) left (right) regular if for every a there is an x in N such that a = xa2 (a = a2x) and a = axa.
Reddy, Y. V., Murty, C. V. L. N.
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On Strongly pi-Regular Rings with Involution
Communications in Mathematics, 2022 Recall that a ring R is called strongly pi-regular if, for every a in R, there is a positive integer n, depending on a, such that a^n belongs to the intersection of a^{n+1}R and Ra^{n+1}. In this paper we give a further study of the notion of a strongly pi-star-regular ring, which is the star-version of strongly pi-regular rings and which was ...
Cui, Jian, Danchev, Peter
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