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The Upper Radical Determined by the Class of all J-Semisimple Subdirectly Irreducible Rings
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作者 杨宗文 王俊民 《Journal of Mathematical Research and Exposition》 CSCD 2000年第4期503-506,共4页
F.A.Szasz has put forward the open problem 55 in [1]: Let K be the class of all subdirectly irreducible rings, whose Jacobson radical is (0). Examine the upper radical determined by the class K. In this paper, the pro... F.A.Szasz has put forward the open problem 55 in [1]: Let K be the class of all subdirectly irreducible rings, whose Jacobson radical is (0). Examine the upper radical determined by the class K. In this paper, the problem has been examined. (1) It has been proved that the upper radical R determined by the class K is a special radical,which lies between Jacobson radical and Brown-McCoy radical. (2) It has been given some necessary and sufficient condition of ring A to be an R-radical ring. 展开更多
关键词 subdirectly irreducible ring special radical antisimple radical MHR-ring Jacobson radical.
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DE MORGAN ALGEBRAS WITH DOUBLE DEMI-PSEUDOCOMPLEMENTATION 被引量:4
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作者 方捷 王雷波 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1613-1623,共11页
The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras (L; ∧ , ∨ , , , + , 0, 1) of type (2, 2, 1, 1, 1, 0, 0) where (L; ∧ , ∨ , , 0, 1) is a de Morgan alge... The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras (L; ∧ , ∨ , , , + , 0, 1) of type (2, 2, 1, 1, 1, 0, 0) where (L; ∧ , ∨ , , 0, 1) is a de Morgan algebra, (L; ∧ , ∨ , , + , 0, 1) is a double demi-p-lattice and the operations x → x , x → x and x → x + are linked by the identities x = x , x + = x + and x + = x + . In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras. 展开更多
关键词 de Morgan algebra double demi-pseudocomplemented algebra subdirectly irreducible
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Congruences on Balanced Pseudocomplemented Ockham Algebras 被引量:1
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作者 Jie FANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第6期1031-1040,共10页
The variety bpO consists of those algebras (L; ∧,∨, f,* ) of type 〈2,2,1, 1,0,0〉 where (L; ∧,∨, f, 0, 1) is an Ockham algebra, (L; ∧,∨, *, 0, 1) is a p-algebra, and the operations x → f(x) and x →... The variety bpO consists of those algebras (L; ∧,∨, f,* ) of type 〈2,2,1, 1,0,0〉 where (L; ∧,∨, f, 0, 1) is an Ockham algebra, (L; ∧,∨, *, 0, 1) is a p-algebra, and the operations x → f(x) and x → x^* satisfy the identities f(x^*) = x^** and [f(x)]^* = f^2(x). In this note, we show that the compact congruences on a bpO-algebra form a dual Stone lattice. Using this, we characterize the algebras in which every principal congruence is complemented. We also give a description of congruence coherent bpO-algebras. 展开更多
关键词 pseudocomplemented algebra Ockham algebra subdirectly irreducible
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Commuting double Ockham algebras
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作者 FANG Jie Department of Mathematics,Shantou University,Shantou 515063,China 《Science China Mathematics》 SCIE 2008年第2期185-194,共10页
In this paper,we study a certain class of double Ockham algebras (L;∧,∨,f,k,0,1), namely the bounded distributive lattices (L;∧,∨,0,1) endowed with a commuting pair of unary op- erations f and k,both of which are ... In this paper,we study a certain class of double Ockham algebras (L;∧,∨,f,k,0,1), namely the bounded distributive lattices (L;∧,∨,0,1) endowed with a commuting pair of unary op- erations f and k,both of which are dual endomorphisms.We characterize the subdirectly irreducible members,and also consider the special case when both (L;f) and (L;k) are de Morgan algebras.We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members, all of which are simple. 展开更多
关键词 subdirectly irreducible double Ockham algebra Priestley duality 06D15 06D30
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Closure Extended Pseudocomplemented MS-Algebras
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作者 LUO Congwen WANG Gaoxia 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2021年第3期249-255,共7页
The variety CPMS of closure extended pseudocomplemented MS-algebras consists of the algebras(L;∧,∨,°,*,+,0,1)of type(2,2,1,1,1,0,0),where(L;∧,∨,°,*,+,0,1)is a pseudocomplemented MS-algebra,+is a lattice ... The variety CPMS of closure extended pseudocomplemented MS-algebras consists of the algebras(L;∧,∨,°,*,+,0,1)of type(2,2,1,1,1,0,0),where(L;∧,∨,°,*,+,0,1)is a pseudocomplemented MS-algebra,+is a lattice endomorphism on L with x≤x^(+)=x^(++)and the operations x→x°,x→x^(*)and x→x^(+)are linked by the identities x^(+*)=x^(*+)and x^(+)°=x°^(+).In this paper,we characterize congruences on a CPMS-algebra,and show that there are precisely eight non-isomorphic subdirectly irreducible nontrivial algebras in the class of these algebras and give a complete description of them. 展开更多
关键词 closure extended pseudocomplemented MS-algebra CONGRUENCE subdirectly irreducible
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Graded Antisimple Primitive Radical
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作者 Jun Chao WEI Li Bin LI Department of Mathematics, College of Science. Yangzhou University. Yangzhon 225002, P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2002年第3期505-512,共8页
We introduce the graded version of the antisimple primitive radical SJ, the graded an- tisimple prinfitive radical SJ_G. We show that SJ_G=SJ_(ref)=SJ^G when |G|<∞. where SJ_(ref) denotes the reflected antisimple ... We introduce the graded version of the antisimple primitive radical SJ, the graded an- tisimple prinfitive radical SJ_G. We show that SJ_G=SJ_(ref)=SJ^G when |G|<∞. where SJ_(ref) denotes the reflected antisimple primitive radical and SJ^G denotes the restricted antisimple primitive radical. Furthermore, we discuss the graded supplementing radical of SJ^G. 展开更多
关键词 Graded antisimple primitive radical Graded subdirectly irreducible graded primitive ring Graded supplementing radical
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Axioms in the Variety of eO-Algebras
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作者 FANG Jie SUN Zhong Ju 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第3期699-705,共7页
The variety eO of extended Ockham algebras consists of those algebras (L; ∧, ∨, f, k, 0, 1) such that (L; ∧, ∨, 0, 1) is a bounded distributive lattice together with a dual endomorphism f on L and an endomorp... The variety eO of extended Ockham algebras consists of those algebras (L; ∧, ∨, f, k, 0, 1) such that (L; ∧, ∨, 0, 1) is a bounded distributive lattice together with a dual endomorphism f on L and an endomorphism k on L such that fk = kf. In this paper we extend Urquhart's theorem to eO-algebras and we are in particular concerned with the subclass e2M of eO-algebras in which f^2 = id and k^2 = id. We show that there are 19 non-equivalent axioms in e2M and then order them by implication. 展开更多
关键词 Extended Ockham algebra dual space subdirectly irreducible algebra equational basis.
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