数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1613-1623.doi: 10.1016/S0252-9602(11)60347-0

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DE MORGAN ALGEBRAS WITH DOUBLE DEMI-PSEUDOCOMPLEMENTATION

方捷|王雷波   

  1. School of Computer Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China Department of Mathematics, Shantou University, Shantou 515063, China
  • 收稿日期:2008-09-29 修回日期:2010-09-29 出版日期:2011-07-20 发布日期:2011-07-20

DE MORGAN ALGEBRAS WITH DOUBLE DEMI-PSEUDOCOMPLEMENTATION

 FANG Jie, WANG Lei-Bo   

  1. School of Computer Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China Department of Mathematics, Shantou University, Shantou 515063, China
  • Received:2008-09-29 Revised:2010-09-29 Online:2011-07-20 Published:2011-07-20

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摘要：

The variety ddpM of de Morgan algebras with double demi-pseudocomplem-entation 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.

关键词: de Morgan algebra, double demi-pseudocomplemented algebra, subdirectly irreducible

Abstract:

The variety ddpM of de Morgan algebras with double demi-pseudocomplem-entation 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.

Key words: de Morgan algebra, double demi-pseudocomplemented algebra, subdirectly irreducible

中图分类号: 

  • 06D15
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